Solving Logarithmic Equations

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

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

Express $y$ in terms of $x$ for the following equation:

$\ln (y+2)-\ln y=1+2\ln x$

Express $y$ in terms of $x$ for the following equation:

$2\ln (y+1)-\ln y=\ln (x+y)$

Solve, giving your answer correct to $3$ significant figures.

$\ln \left(2+x^2\right)=1+2\ln x$

Solve, giving your answer correct to $3$ significant figures.

$\ln (x+2)-\ln x=1$

Solve, giving your answer correct to $3$ significant figures.

$\ln (2x+1)=2\ln x+\ln 5$

Solve, giving your answer correct to $3$ significant figures.

$2\ln (x+1)=\ln (2x+3)$

Solve, giving your answer correct to $3$ significant figures.

$2\ln (x+2)-\ln x=\ln (2x-1)$

Solve, giving your answer correct to $3$ significant figures.

$\ln \left(3-x^2\right)=2\ln x$

Solve, giving your answer correct to $3$ significant figures.

$\ln (2x+1)=-2$

Solve, giving your answer correct to $3$ significant figures.

$\ln (x-2)=6$

Solve, giving your answer correct to $3$ significant figures.

$\ln x=-4$

Solve, giving your answer correct to $3$ significant figures.

$\ln x=5$

Solve ${\log }_{x}49=2$.

Solve ${\log }_{4}x=0$.

Solve ${\log }_{3}x=2$.

Solve ${\log }_{2}x=3$.

Solve the equation, giving your answers correct to $3$ significant figures.

${\log }_{10}x=-1.4$

Solve the equation, giving your answers correct to $3$ significant figures.

${\log }_{10}x=2.76$