Moderate -0.8 This is a straightforward logarithm application question requiring only the standard technique of taking logs of both sides, using log laws to bring down powers, and solving a linear equation. It's routine A-level work with no problem-solving element, making it easier than average, though not trivial since it requires correct manipulation of logarithmic expressions.
Take logs of both sides – allow any (consistent) base including natural logs
\((3x - 1) = (x + 4)\log_2 3 \Rightarrow x = K\)
M1
Bring both powers to the front and attempt to make \(x\) the subject
\(x = \frac{4\log_2 3 + 1}{3 - \log_2 3} = 5.19\)
A1
In base 10: \(x = \frac{4\log 3 + \log 2}{3\log 2 - \log 3} = 5.19\)
$2^{3x-1} = 3^{x+4} \Rightarrow 3x - 1 = \log_2(3^{x+4})$ | M1 | Take logs of both sides – allow any (consistent) base including natural logs
$(3x - 1) = (x + 4)\log_2 3 \Rightarrow x = K$ | M1 | Bring both powers to the front and attempt to make $x$ the subject
$x = \frac{4\log_2 3 + 1}{3 - \log_2 3} = 5.19$ | A1 | In base 10: $x = \frac{4\log 3 + \log 2}{3\log 2 - \log 3} = 5.19$
Use logarithms to solve the equation $2^{3x-1} = 3^{x+4}$, giving your answer correct to 3 significant figures. [3]
\hfill \mbox{\textit{OCR H240/03 2018 Q1 [3]}}