Question

Express each of the following in logarithmic form ​

Answer 1

See explanation.

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.

Answer 2

`\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)}`

Explanation:

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

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

Explanation:

`3^(-2)=(1)/(9)\qquad \rightarrow \qquad -2=log_3 \bigg((1)/(9)\bigg)`

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

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{(3)/(4)=log_(81) (27)}`

Explanation:

`81^{(3)/(4)}=27\qquad \rightarrow \qquad (3)/(4)=log_(81) (27)`