91Ó°ÊÓ

Evaluate or simplify each expression without using a calculator. $$ e^{\ln 5 x^{2}} $$

In Exercises \(89-102,\) determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. $$ \log (x+3)-\log (2 x)=\frac{\log (x+3)}{\log (2 x)} $$

Evaluate or simplify each expression without using a calculator. $$ e^{\ln 7 x^{2}} $$

In Exercises \(89-102,\) determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. $$ \log _{6}\left(\frac{x-1}{x^{2}+4}\right)=\log _{6}(x-1)-\log _{6}\left(x^{2}+4\right) $$

Solve each equation. $$ \ln (2 x+1)+\ln (x-3)-2 \ln x=0 $$

Solve each equation. $$ \ln 3-\ln (x+5)-\ln x=0 $$

In Exercises \(89-102,\) determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. $$ \log _{6}[4(x+1)]=\log _{6} 4+\log _{6}(x+1) $$

Write each equation in its equivalent exponential form. Then solve for \(x .\) $$ \log _{3}(x-1)=2 $$

In Exercises \(89-102,\) determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. $$ \log _{3} 7=\frac{1}{\log _{7} 3} $$

Solve each equation. $$ 5^{x^{2}-12}=25^{2 x} $$