Easy -1.2 This is a straightforward exponential equation requiring only basic logarithm manipulation: divide by 4, then apply logarithms to get x = ln(5/4)/ln(3). It's a single-step problem testing routine technique with no conceptual difficulty or problem-solving required, making it easier than average.
Allow using logs before rearranging, as long as valid method to deal with \(\log(4 \times 3^x)\). Take logarithms and apply at least one log rule correctly. Rearrange to make \(x\) the subject. Obtain correct answer aef. Allow BOD if no base specified. ISW decimal answer but not subsequent incorrect log work, such as \(\log(\frac{5}{4})/\log(3) = \log(\frac{5}{12})\).
$3^x = \frac{5}{4}$ | B1* | State $3^x = \frac{5}{4}$
$x = \log_3(\frac{5}{4})$ | M1d*, M1d*, A1 [4] | Allow using logs before rearranging, as long as valid method to deal with $\log(4 \times 3^x)$. Take logarithms and apply at least one log rule correctly. Rearrange to make $x$ the subject. Obtain correct answer aef. Allow BOD if no base specified. ISW decimal answer but not subsequent incorrect log work, such as $\log(\frac{5}{4})/\log(3) = \log(\frac{5}{12})$.