1 of 8 0-day streak

Apply logarithm laws and inverse identities

Question 1 of 8

No calculator

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

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

Keep all coefficients and exponents in exact form

(a)1 mark

Select the expression equivalent to the displayed expression

\log_{\frac{2}{3}}\left(\frac{3}{2}\right)\cdot \log_{\frac{2}{3}}\left(\frac{2}{3}\right)

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

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

\log_{\frac{2}{3}}\left(\frac{3}{2}\right) - \log_{\frac{2}{3}}\left(\frac{2}{3}\right)

(b)4 marks

Fill in the numerical data for the logarithm terms

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

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

Evaluate the original expression exactly

exact value