1 of 8 0-day streak

Apply logarithm laws and inverse identities

Question 1 of 8

No calculator

The common base is \(\frac{3}{2}\); it is positive and is not 1. Every logarithm argument shown is positive

\log_{\frac{3}{2}}\left(\frac{\frac{9}{4}}{\frac{3}{2}}\right)

Give exact values. The logarithm base is the same throughout

(a)1 mark

Which displayed form has the same value as the expression above?

3

1

\log_{\frac{3}{2}}\left(\frac{9}{4} + \frac{3}{2}\right)

-2

(b)4 marks

Record the exact coefficient and base exponent for each displayed logarithm term

\log_{\frac{3}{2}}\left(\frac{\frac{9}{4}}{\frac{3}{2}}\right)

exponent in argument 2 coefficient of logarithm 1 exponent in argument 1 coefficient of logarithm 2

Find the exact value of the displayed expression

exact value