d log_(1/2)(1/4) = −2 e log₈ 8 = 1 i log₇ 7 = 0 g log₁.5 2.25 = 2

Question

ScanSolve AI Tutor · Accepted Answer

voici les solutions pour la section F. F) Change the following logarithmic form into index form The general conversion from logarithmic form log_b M = N to index form is b^N = M. d) log_(1/2) (1/4) = −2 Converting to index form: (1/2)⁻² = 1/4; e) log₈ 8 = 1 Converting to index form: 8¹ = 8; f) log₃ 1 = 0 Converting to index form: 3⁰ = 1; g) log_(1.5) 2.25 = 2 Converting to index form: (1.5)² = 2.25 h) log₅ (1/125) This is an expression. To convert it to index form, we first need to find its value. Step 1: Let log₅ (1/125) = N. 5^N = 1/125 Step 2: Express 1/125 as a power of 5. 5^N = (1)/(5³); 5^N = 5⁻³ Step 3: Equate the exponents to find N. N = −3; So, the logarithmic form is log₅ (1/125) = −3. Converting this to index form: 5⁻³ = 1/125

d log_(1/2)(1/4) = -2 e log_8 8 = 1 i log_7 7 = 0 g log_1.5 2.25 = 2

Answers

Step-by-step solution

Part d

Part e
$8^1 = 8$

Part f
$3^0 = 1$

Part g
$(1.5)^2 = 2.25$

Part h· 3 steps
$5^{-3} = \frac{1}{125}$

Let $\log_5 (1/125) = N$ .

Express $1/125$ as a power of 5.

Equate the exponents to find $N$ .

Try one yourself

Still stuck on this one?

More Mathematics Questions

d log_(1/2)(1/4) = -2 e log_8 8 = 1 i log_7 7 = 0 g log_1.5 2.25 = 2

Answers

Step-by-step solution

Part d

Part e81=88^1 = 881=8

Part f30=13^0 = 130=1

Part g(1.5)2=2.25(1.5)^2 = 2.25(1.5)2=2.25

Part h· 3 steps5−3=11255^{-3} = \frac{1}{125}5−3=1251​

Let log⁡5(1/125)=N\log_5 (1/125) = Nlog5​(1/125)=N.

Express 1/1251/1251/125 as a power of 5.

Equate the exponents to find NNN.