So we have the equation [tex]3log2^{x}=27[/tex], and we want to solve for [tex]x[/tex].
First, we are going to apply the log of a power rule: [tex]loga^{x}=xloga[/tex]
[tex]3log2^{x}=27[/tex]
[tex]3xlog2=27[/tex]
Next, we are going to divide both sides of the equation by [tex]3log2[/tex]:
[tex]3xlog2=27[/tex]
[tex] \frac{3xlog2}{3log2} = \frac{27}{3log2} [/tex]
[tex]x= \frac{27}{3log2} [/tex]
Last but not least, we can use a calculator to evaluate the right hand side of the equation:
[tex]x= \frac{27}{3log2} [/tex]
[tex]x=29.8974[/tex]
We can conclude that the solution of our logarithmic function is [tex]x=29.8974[/tex]. I don't know who told you that the correct answer is 8, but they is wrong.
