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{16}{81}}{\frac{81}{16}}\right)

Use the logarithm laws and inverse identities shown by the expression

(a)1 mark

Choose the exact form obtained from the logarithm identities

\log_{\frac{3}{2}}\left(\frac{16}{81} + \frac{81}{16}\right)

-8

16

8

(b)4 marks

Complete the table with the coefficients and argument exponents used in the calculation

\log_{\frac{3}{2}}\left(\frac{\frac{16}{81}}{\frac{81}{16}}\right)

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

Calculate the exact result

exact value