Solve 2P=Pe^0.07T

$$2 P = P e ^ { 0.07 T }$$

Solve for P

$$\left\{\begin{matrix}\\P=0\text{, }&\text{unconditionally}\\P\in \mathrm{R}\text{, }&T=\frac{100\ln(2)}{7}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract Pe^{0.07T} from both sides.

$$2P-Pe^{0.07T}=0$$

Reorder the terms.

$$-Pe^{0.07T}+2P=0$$

Combine all terms containing P.

$$\left(-e^{0.07T}+2\right)P=0$$

The equation is in standard form.

$$\left(2-e^{\frac{7T}{100}}\right)P=0$$

Divide 0 by 2-e^{0.07T}.

$$P=0$$

Solve for T

$$\left\{\begin{matrix}\\T=\frac{100\ln(2)}{7}\text{, }&\text{unconditionally}\\T\in \mathrm{R}\text{, }&P=0\end{matrix}\right.$$

Steps Using Definition of Logarithm

Swap sides so that all variable terms are on the left hand side.

$$Pe^{0.07T}=2P$$

Divide both sides by P.

$$e^{0.07T}=2$$

Take the logarithm of both sides of the equation.

$$\log(e^{0.07T})=\log(2)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$0.07T\log(e)=\log(2)$$

Divide both sides by \log(e).

$$0.07T=\frac{\log(2)}{\log(e)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$0.07T=\log_{e}\left(2\right)$$

Divide both sides of the equation by 0.07, which is the same as multiplying both sides by the reciprocal of the fraction.

$$T=\frac{\ln(2)}{0.07}$$