[tex]\text{Use the exponent-to-log rule: }\quad y=b^x\quad \rightarrow \quad log_b\ (y)=x[/tex]
(i) Answer: [tex]\bold{3=log_5 (125)}[/tex]
Step-by-step explanation:
[tex]5^3=125\qquad \rightarrow \qquad 3=log_5 (125)[/tex]
(ii) Answer: [tex]\bold{-2=log_{3} \bigg(\dfrac{1}{9}\bigg)}[/tex]
Step-by-step explanation:
[tex]3^{-2}=\dfrac{1}{9}\qquad \rightarrow \qquad -2=log_3 \bigg(\dfrac{1}{9}\bigg)[/tex]
(iii) Answer: [tex]\bold{-3=log (0.001)}[/tex]
Step-by-step explanation:
[tex]10^{-3}=0.001\qquad \rightarrow \qquad -3=log_{10} (0.001)[/tex]
[tex]\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)}[/tex]
(iv) Answer: [tex]\bold{\dfrac{3}{4}=log_{81} (27)}[/tex]
Step-by-step explanation:
[tex]81^{\dfrac{3}{4}}=27\qquad \rightarrow \qquad \dfrac{3}{4}=log_{81} (27)[/tex]
