Rewrite the following equations in logarithmic form: a) y = x^(1/2) b) y = 120 × 3^x

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ScanSolve AI Tutor · Accepted Answer

a) Step 1: Rewrite the square root as a fractional exponent. y = x^(1/2) Step 2: Take the logarithm base 10 of both sides of the equation. log₁₀ y = log₁₀ (x^(1/2)); Step 3: Apply the power rule of logarithms, log_b (M^c) = c log_b M. log₁₀ y = 1/2 log₁₀ x The logarithmic equation is: log₁₀ y = 1/2 log₁₀ x b) Step 1: Take the logarithm base 10 of both sides of the equation. log₁₀ y = log₁₀ (120 × 3^x); Step 2: Apply the product rule of logarithms, log_b (MN) = log_b M + log_b N, to the right side. log₁₀ y = log₁₀ 120 + log₁₀ (3^x); Step 3: Apply the power rule of logarithms, log_b (M^c) = c log_b M, to the term log₁₀ (3^x). log₁₀ y = log₁₀ 120 + x log₁₀ 3 The logarithmic equation is: log₁₀ y = log₁₀ 120 + x log₁₀ 3

Rewrite the following equations in logarithmic form: a) y = x^(1/2) b) y = 120 * 3^x

Answers

Step-by-step solution

Part a· 2 steps

Take the logarithm base 10 of both sides of the equation.

Apply the power rule of logarithms, $\log_b (M^c) = c \log_b M$ .

Part b· 2 steps
$\log_{10} y = \log_{10} 120 + x \log_{10} 3$

Apply the product rule of logarithms, $\log_b (MN) = \log_b M + \log_b N$ , to the right side.

Apply the power rule of logarithms, $\log_b (M^c) = c \log_b M$ , to the term $\log_{10} (3^x)$ .

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