Solving Logarithmic equations in Arithmetic form with Different bases Questions with solutions

In logarithms, solving the logarithm equations in arithmetic form quantities with different bases is one type of logarithmic problems. The worksheet on solving the logarithmic equations in arithmetic form with different bases is given here for students to practice, and the solutions with answers to learn how to solve the logarithm equations in arithmetic form quantities with different bases by the log formulas.

Solve $\log_{\large \frac{1}{2}}{\Big(\log_{\large x}{\big(\log_{4}{(32)}\big)}\Big)}$ $\,=\,$ $2$

Solve $\log_{2}{x}$ $+$ $\log_{4}{x}$ $+$ $\log_{16}{x}$ $\,=\,$ $7$

Solve $\log_{\sqrt{2}}{\Big(\log_{\large 2}{\big(\log_{4}{(x-15)}\big)}\Big)}$ $\,=\,$ $0$

Solve $\log_{2}{x}$ $+$ $\log_{4}{x}$ $+$ $\log_{8}{x}$ $\,=\,$ $11$