Question Type 7: Using change of base formula Bootcamps

Express $\log_5(7)$ in terms of natural logarithms.

Express $\log_8(18)$ in terms of $\log_2(3)$.

Evaluate the expression $\displaystyle \frac{3}{\log_2(8)}+\frac{2}{\log_4(16)}.$

Simplify the expression $\displaystyle \frac{3}{\log_2(x)} + \log_x(y)$ into a form involving $\ln x$ and $\ln y$.

Simplify the expression $\frac{2}{\log_5(7)}-\log_7(25)$ into a form involving natural logarithms.

Simplify $\displaystyle \log_3(16) + \frac{2}{\log_4(3)}$ into a single quotient of natural logarithms.

Simplify $\displaystyle \log_2(9) - \frac{2}{\log_3(2)}$ into an expression involving $\ln2$ and $\ln3$.

If $\log_3(b)=4$, evaluate $\log_{27}(b)$.

Express $\log_4(27)$ in terms of $\log_2(3)$.

Solve for $x>0$, $x\neq1$: $\frac{3}{\log_2(x)}+\log_x(16)=5.$

Show that for $a>0$, $b>0$, $a\neq1$, $b\neq1$: $\log_a(b)\,\log_b(a)=1.$

Solve for $x>0$: $\log_2(x)+\log_4(x)+\log_8(x)=6.$

Solve for $x>0$, $x\neq1$: $\log_x(81)+\frac{4}{\log_3(x)}=6.$