1 of 8 0-day streak

Apply logarithm laws and inverse identities

Question 1 of 8

No calculator

The common base is \(4\); it is positive and is not 1. Every logarithm argument shown is positive

\log_{4}\left(\frac{\frac{1}{256}}{64}\right)

Use the logarithm laws and inverse identities shown by the expression

(a)1 mark

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

-7

7

12

\log_{4}\left(\frac{1}{256} + 64\right)

(b)4 marks

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

\log_{4}\left(\frac{\frac{1}{256}}{64}\right)

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

Find the exact value of the displayed expression

exact value