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TiliK225 [7]
2 years ago
13

Express each of the following in logarithmic form ​

Mathematics
2 answers:
worty [1.4K]2 years ago
8 0

\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)}

<u>Step-by-step explanation:</u>

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

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

<u>Step-by-step explanation:</u>

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

(iii) Answer:   \bold{-3=log (0.001)}

<u>Step-by-step explanation:</u>

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)}

<u>Step-by-step explanation:</u>

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

vodomira [7]2 years ago
5 0

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.

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