Solve for question one to 9

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for questions 1 to 9. Question 1: 2 log_b 4 − 2/3 log_b 8 + log_b 2 = log_b x; Step 1: Apply the power rule c log_b a = log_b (a^c) to the first two terms. log_b (4²) − log_b (8^(2/3)) + log_b 2 = log_b x; log_b 16 − log_b (√[3]8)² + log_b 2 = log_b x; log_b 16 − log_b (2²) + log_b 2 = log_b x; log_b 16 − log_b 4 + log_b 2 = log_b x; Step 2: Apply the quotient rule log_b M − log_b N = log_b (M/N) to the first two terms. log_b (16/4) + log_b 2 = log_b x; log_b 4 + log_b 2 = log_b x; Step 3: Apply the product rule log_b M + log_b N = log_b (M × N) to the left side. log_b (4 × 2) = log_b x; log_b 8 = log_b x Step 4: Equate the arguments since the bases are the same. x = 8 Question 2: 2 log_b 3 + log_b 5 − log_b 9 = log_b x; Step 1: Apply the power rule c log_b a = log_b (a^c) to the first term. log_b (3²) + log_b 5 − log_b 9 = log_b x; log_b 9 + log_b 5 − log_b 9 = log_b x Step 2: Combine terms. (log_b 9 − log_b 9) + log_b 5 = log_b x; 0 + log_b 5 = log_b x; log_b 5 = log_b x Step 3: Equate the arguments. x = 5 Question 3: log_b 16 − log_b 2 + log_b 4 = log_b x; Step 1: Apply the quotient rule log_b M − log_b N = log_b (M/N) to the first two terms. log_b (16/2) + log_b 4 = log_b x; log_b 8 + log_b 4 = log_b x; Step 2: Apply the product rule log_b M + log_b N = log_b (M × N) to the left side. log_b (8 × 4) = log_b x; log_b 32 = log_b x Step 3: Equate the arguments. x = 32 Question 4: log_b 25 + log_b 4 − log_b 10 = log_b x; Step 1: Apply the product rule log_b M + log_b N = log_b (M × N) to the first two terms. log_b (25 × 4) − log_b 10 = log_b x; log_b 100 − log_b 10 = log_b x; Step 2: Apply the quotient rule log_b M − log_b N = log_b (M/N) to the left side. log_b (100/10) = log_b x; log_b 10 = log_b x Step 3: Equate the arguments. x = 10 Question 5: log_b 12 − log_b 3 + log_b 2 = log_b x; Step 1: Apply the quotient rule log_b M − log_b N = log_b (M/N) to the first two terms. log_b (12/3) + log_b 2 = log_b x; log_b 4 + log_b 2 = log_b x; Step 2: Apply the product rule log_b M + log_b N = log_b (M × N) to the left side. log_b (4 × 2) = log_b x; log_b 8 = log_b x Step 3: Equate the arguments. x = 8 Question 6: log_b 100 − log_b 5 + log_b 2 = log_b x; Step 1: Apply the quotient rule log_b M − log_b N = log_b (M/N) to the first two terms. log_b (100/5) + log_b 2 = log_b x; log_b 20 + log_b 2 = log_b x; Step 2: Apply the product rule log_b M + log_b N = log_b (M × N) to the left side. log_b (20 × 2) = log_b x; log_b 40 = log_b x Step 3: Equate the arguments. x = 40 Question 7: log_b 18 + log_b 2 − log_b 4 = log_b x; Step 1: Apply the product rule log_b M + log_b N = log_b (M × N) to the first two terms. log_b (18 × 2) − log_b 4 = log_b x; log_b 36 − log_b 4 = log_b x; Step 2: Apply the quotient rule log_b M − log_b N = log_b (M/N) to the left side. log_b (36/4) = log_b x; log_b 9 = log_b x Step 3: Equate the arguments. x = 9 Question 8: log_b 24 − log_b 3 + log_b 5 = log_b x; Step 1: Apply the quotient rule log_b M − log_b N = log_b (M/N) to the first two terms. log_b (24/3) + log_b 5 = log_b x; log_b 8 + log_b 5 = log_b x; Step 2: Apply the product rule log_b M + log_b N = log_b (M × N) to the left side. log_b (8 × 5) = log_b x; log_b 40 = log_b x Step 3: Equate the arguments. x = 40 Question 9: log_b 15 + log_b 2 − log_b 6 = log_b x; Step 1: Apply the product rule log_b M + log_b N = log_b (M × N) to the first two terms. log_b (15 × 2) − log_b 6 = log_b x; log_b 30 − log_b 6 = log_b x; Step 2: Apply the quotient rule log_b M − log_b N = log_b (M/N) to the left side. log_b (30/6) = log_b x; log_b 5 = log_b x Step 3: Equate the arguments. x = 5

Solve for question one to 9

Step-by-step solution

Part 1· 4 steps

Apply the power rule clog⁡ba=log⁡b(ac)c \log_b a = \log_b (a^c)clogb​a=logb​(ac) to the first two terms.

Apply the quotient rule log⁡bM−log⁡bN=log⁡b(MN)\log_b M - \log_b N = \log_b \left(\frac{M}{N}\right)logb​M−logb​N=logb​(NM​) to the first two terms.

Apply the product rule log⁡bM+log⁡bN=log⁡b(M×N)\log_b M + \log_b N = \log_b (M \times N)logb​M+logb​N=logb​(M×N) to the left side.

Equate the arguments since the bases are the same.

Part 2· 3 steps

Apply the power rule clog⁡ba=log⁡b(ac)c \log_b a = \log_b (a^c)clogb​a=logb​(ac) to the first term.

Combine terms.

Equate the arguments.

Part 3· 3 steps

Apply the quotient rule log⁡bM−log⁡bN=log⁡b(MN)\log_b M - \log_b N = \log_b \left(\frac{M}{N}\right)logb​M−logb​N=logb​(NM​) to the first two terms.

Apply the product rule log⁡bM+log⁡bN=log⁡b(M×N)\log_b M + \log_b N = \log_b (M \times N)logb​M+logb​N=logb​(M×N) to the left side.

Equate the arguments.

Part 4· 3 steps

Apply the product rule log⁡bM+log⁡bN=log⁡b(M×N)\log_b M + \log_b N = \log_b (M \times N)logb​M+logb​N=logb​(M×N) to the first two terms.

Apply the quotient rule log⁡bM−log⁡bN=log⁡b(MN)\log_b M - \log_b N = \log_b \left(\frac{M}{N}\right)logb​M−logb​N=logb​(NM​) to the left side.

Equate the arguments.

Part 5· 3 steps

Apply the quotient rule log⁡bM−log⁡bN=log⁡b(MN)\log_b M - \log_b N = \log_b \left(\frac{M}{N}\right)logb​M−logb​N=logb​(NM​) to the first two terms.

Apply the product rule log⁡bM+log⁡bN=log⁡b(M×N)\log_b M + \log_b N = \log_b (M \times N)logb​M+logb​N=logb​(M×N) to the left side.

Equate the arguments.

Part 6· 3 steps

Apply the quotient rule log⁡bM−log⁡bN=log⁡b(MN)\log_b M - \log_b N = \log_b \left(\frac{M}{N}\right)logb​M−logb​N=logb​(NM​) to the first two terms.

Apply the product rule log⁡bM+log⁡bN=log⁡b(M×N)\log_b M + \log_b N = \log_b (M \times N)logb​M+logb​N=logb​(M×N) to the left side.

Equate the arguments.

Part 7· 3 steps

Apply the product rule log⁡bM+log⁡bN=log⁡b(M×N)\log_b M + \log_b N = \log_b (M \times N)logb​M+logb​N=logb​(M×N) to the first two terms.

Apply the quotient rule log⁡bM−log⁡bN=log⁡b(MN)\log_b M - \log_b N = \log_b \left(\frac{M}{N}\right)logb​M−logb​N=logb​(NM​) to the left side.

Equate the arguments.

Part 8· 3 steps

Apply the quotient rule log⁡bM−log⁡bN=log⁡b(MN)\log_b M - \log_b N = \log_b \left(\frac{M}{N}\right)logb​M−logb​N=logb​(NM​) to the first two terms.

Apply the product rule log⁡bM+log⁡bN=log⁡b(M×N)\log_b M + \log_b N = \log_b (M \times N)logb​M+logb​N=logb​(M×N) to the left side.

Equate the arguments.

Part 9· 3 steps

Apply the product rule log⁡bM+log⁡bN=log⁡b(M×N)\log_b M + \log_b N = \log_b (M \times N)logb​M+logb​N=logb​(M×N) to the first two terms.

Apply the quotient rule log⁡bM−log⁡bN=log⁡b(MN)\log_b M - \log_b N = \log_b \left(\frac{M}{N}\right)logb​M−logb​N=logb​(NM​) to the left side.

Equate the arguments.

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More Mathematics Questions

Apply the power rule $c \log_b a = \log_b (a^c)$ to the first two terms.

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