Solve e^p+3-6=5

$$e ^ { p + 3 } - 6 = 5$$

Solve for p

$$p=\ln(11)-3\approx -0.602104727$$

Steps Using Definition of Logarithm

Use the rules of exponents and logarithms to solve the equation.

$$e^{p+3}-6=5$$

Add 6 to both sides of the equation.

$$e^{p+3}=11$$

Take the logarithm of both sides of the equation.

$$\log(e^{p+3})=\log(11)$$

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

$$\left(p+3\right)\log(e)=\log(11)$$

Divide both sides by \log(e).

$$p+3=\frac{\log(11)}{\log(e)}$$

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

$$p+3=\log_{e}\left(11\right)$$

Subtract 3 from both sides of the equation.

$$p=\ln(11)-3$$