Answer: (a) \(w=2.54\). (b) \(x=8\) or \(x=27\).

Answer: (a) \(w=2.54\). (b) \(x=8\) or \(x=27\).

(a) Take logarithms of both sides:

\((w-1)\ln 5=\ln 12\).

Hence

\(w=1+\frac{\ln 12}{\ln 5}=2.543\ldots\).

So, to 2 decimal places,

\(w=2.54\).

(b) Let \(u=x^{1/3}\). Then \(x^{2/3}=u^2\), so the equation becomes

\(u^2-5u+6=0\).

Factorising gives

\((u-2)(u-3)=0\),

so \(u=2\) or \(u=3\).

Since \(u=x^{1/3}\),

\(x=2^3=8\) or \(x=3^3=27\).