1 of 8 0-day streak

Express one logarithmic quantity in terms of another

Question 1 of 8

No calculator

Let \(z=\log_{4}\left(s\right)\). The variable \(s\) is positive. The base \(4\) and every displayed logarithm base are positive and are not 1

4\log_{\left(4\right)^{2}}\left(\left(4\right)^{2}\,s^{-1}\right) - 3\log_{\left(4\right)^{3}}\left(\left(4\right)^{-2}\,s^{-1}\right)

Use exact logarithm laws and change of base

(a)1 mark

Which form gives the displayed quantity using \(z\)?

34 + z

\frac{1}{3} - \frac{5}{6}z

6 - z

6 - s

(b)6 marks

Complete the table with the exact numerical coefficients and argument exponents

4\log_{\left(4\right)^{2}}\left(\left(4\right)^{2}\,s^{-1}\right) - 3\log_{\left(4\right)^{3}}\left(\left(4\right)^{-2}\,s^{-1}\right)

outside coefficient 1 outside coefficient 2 exponent of the base in argument 2 exponent of the base in argument 1 exponent of the original variable in argument 2 exponent of the original variable in argument 1