Solve 24 + e ^ (2x) = 45 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$24+e^{2x}=45$$

Solve for x

$x=\frac{\ln(21)}{2}\approx 1.522261219$

Steps Using Definition of Logarithm

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

$$e^{2x}+24=45$$

Subtract $24$ from both sides of the equation.

$$e^{2x}=21$$

Take the logarithm of both sides of the equation.

$$\log(e^{2x})=\log(21)$$

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

$$2x\log(e)=\log(21)$$

Divide both sides by $\log(e)$.

$$2x=\frac{\log(21)}{\log(e)}$$

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

$$2x=\log_{e}\left(21\right)$$

Divide both sides by $2$.

$$x=\frac{\ln(21)}{2}$$

Solve for x (complex solution)

$x=\frac{\ln(21)}{2}+i\pi n_{1}$
$n_{1}\in \mathrm{Z}$