Question

Please help!! solve the exponential equation. Express the solution in terms of natural logarithms. Then use a calculator to obtain decimal approximation for the solution. what is the solution in terms of natural logarithms?5e^7x=775

Answer 1

\(\bf 5e^{7x}=775\implies e^{7x}=\cfrac{775}{5}\implies e^{7x}=155\\ \quad \\ \quad \\
\textit{log cancellation rule of }\quad \color{blue}{log_aa^x=x}\qquad thus\\ \quad \\
e^{7x}=155\implies log_e(e^{7x})=log_e(155)\implies 7x=log_e(155)\)

Answer 2

so solve for "x"