Trouble with log question

Question

I'm doing this question from a past papers and I came across this log question. The question says write the following logarithmic expression as a single logarithm to base 10 and I have made numberous attempts trying to solve this equation. The question is shown below.

The second part bit (underneath) is the solution but i dont know how they got from the question to the (9+2/3) part

Thanks, Neamus

Answer 1

There is a mistake in there.

$9\log_2 x + 2\log_8 x = 9\frac {\log x}{\log 2} + 2\frac {\log x}{\log 8}\\ \log 8 = \log 2^3 = 3\log 2\\ 9\frac {\log x}{\log 2} + 2\frac {\log x}{3\log 2}\\ (9+ \frac 23)\frac {\log x}{\log 2}\\ $

Your worksheet is missing the $\log 2$ in the denominator.

And I hope that this sufficiently covers the missing step.

Answer 2

I think you need to write the following. $$\frac{29\log{x}}{3\log2}$$ It's all.