Find the sum and product of all possible values of which makes the following…

MATHEMATICS · Subjective · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

Find the sum and product of all possible values of

x

which makes the following statement true

\log_6 54 + \log_x 16 = \log_{\sqrt{2}} x - \log_{36} \left( \frac{4}{9} \right).