Solve 2 ) 7 ^ (x - 3) = 1 | 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

$$7 ^ { x - 3 } = 1$$

Solve for x

$x=3$

Steps Using Definition of Logarithm

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

$$7^{x-3}=1$$

Take the logarithm of both sides of the equation.

$$\log(7^{x-3})=\log(1)$$

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

$$\left(x-3\right)\log(7)=\log(1)$$

Divide both sides by $\log(7)$.

$$x-3=\frac{\log(1)}{\log(7)}$$

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

$$x-3=\log_{7}\left(1\right)$$

Add $3$ to both sides of the equation.

$$x=-\left(-3\right)$$

Solve for x (complex solution)

$x=\frac{i\times 2\pi n_{1}}{\ln(7)}+3$
$n_{1}\in \mathrm{Z}$