Question

Solve the exponential inequality.
* Note: B5=base 5

logB5 x-7 is greater than or equal to -6

Answer 1

@mathmale

Answer 2

\(\Large \bf { log_5(x-7) \ge -6
\\ \quad \\
\textit{using the log cancellation rule of }{\color{blue}{ a^{log_ax}=x}}\qquad thus
\\ \quad \\
log_5(x-7) \ge -6\implies {\color{blue}{ 5}}^{log_{\color{blue}{ 5}}(x-7)} \ge {\color{blue}{ 5}}^{-6}\\ \quad \\\implies x-7 \ge 5^{-6} }\)

and I think you can take it from there