Question

Express each of the following in logarithmic form ​

Answer 1

$\text{Use the exponent-to-log rule: }\quad y=b^x\quad \rightarrow \quad log_b\ (y)=x$

(i) Answer:   $\bold{3=log_5 (125)}$

Step-by-step explanation:

$5^3=125\qquad \rightarrow \qquad 3=log_5 (125)$

(ii) Answer:   $\bold{-2=log_{3} \bigg(\dfrac{1}{9}\bigg)}$

Step-by-step explanation:

$3^{-2}=\dfrac{1}{9}\qquad \rightarrow \qquad -2=log_3 \bigg(\dfrac{1}{9}\bigg)$

(iii) Answer:   $\bold{-3=log (0.001)}$

Step-by-step explanation:

$10^{-3}=0.001\qquad \rightarrow \qquad -3=log_{10} (0.001)$

$\text{Note: }log_{10}\text{ is generally written without the subscript.}\\\text{It is similar to writing an exponent of 1. We would write }x^1\text{ as x}.\\\text{We write }log_{10}(y)\text{ as log(y)}$

(iv) Answer:   $\bold{\dfrac{3}{4}=log_{81} (27)}$

Step-by-step explanation:

$81^{\dfrac{3}{4}}=27\qquad \rightarrow \qquad \dfrac{3}{4}=log_{81} (27)$

Answer 2

Answer:

See explanation.

Step-by-step explanation:

(i)  5^3 = 125

log 5^3 = log 125

Using the rule log a^n = n log a

3 log 5 = log 125.

(ii) 3^-2 = 1/9

-2 log 3 = log 1/9

(iii)   10^-3 = 0.001

-3 log 10 = log 0.001

(iv)   81^3/4 = 27

3/4 log 81 = log 27.