Solve, giving your answer in exact form.

$e^{2x}+2e^x-15=0$

Solve, giving your answer in exact form.

$e^{2x}-5e^x+6=0$

Solve, giving your answer in exact form.

$6e^{2x}-13e^x-5=0$

Solve, giving your answer in exact form.

$e^x-21e^{-x}=4$

 Given that the function $f$ is defined as $f:x\mapsto 5e^x+2$ for $x\in R$, find an expression for $f^{-1}\left(x\right)$.

Solve $2\ln \left(3-e^{2x}\right)=1$, giving your answers correct to $3$ significant figures.

Use $\ln \left(1.35127\right)=0.301051$.

Solve the simultaneous equations, giving your answer in exact form.

$2\ln x+\ln y=1+\ln 5$

$\ln 10x-\ln y=2+\ln 2$

Solve the simultaneous equations, giving your answer in exact form.

$e^{3x+4y}=2e^{2x-y}$

$e^{2x+y}=8e^{x+6y}$

Solve $\ln (2x+1)\le \ln (x+4)$.