Algebra Examples

$7^{x - 1} + 7 = 8$

Step 1

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 1.1

Subtract $7$ from both sides of the equation.

$7^{x - 1} = 8 - 7$

Step 1.2

Subtract $7$ from $8$ .

$7^{x - 1} = 1$

Step 2

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

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

Step 3

Expand $\ln (7^{x - 1})$ by moving $x - 1$ outside the logarithm.

$(x - 1) \ln (7) = \ln (1)$

Step 4

Simplify the left side.

Tap for more steps...

Step 4.1

Simplify $(x - 1) \ln (7)$ .

Tap for more steps...

Step 4.1.1

Apply the distributive property.

$x \ln (7) - 1 \ln (7) = \ln (1)$

Step 4.1.2

Rewrite $- 1 \ln (7)$ as $- \ln (7)$ .

$x \ln (7) - \ln (7) = \ln (1)$

Step 5

Simplify the right side.

Tap for more steps...

Step 5.1

The natural logarithm of $1$ is $0$ .

$x \ln (7) - \ln (7) = 0$

Step 6

Add $\ln (7)$ to both sides of the equation.

$x \ln (7) = \ln (7)$

Step 7

Divide each term in $x \ln (7) = \ln (7)$ by $\ln (7)$ and simplify.

Tap for more steps...

Step 7.1

Divide each term in $x \ln (7) = \ln (7)$ by $\ln (7)$ .

$\frac{x \ln (7)}{\ln (7)} = \frac{\ln (7)}{\ln (7)}$

Step 7.2

Simplify the left side.

Tap for more steps...

Step 7.2.1

Cancel the common factor of $\ln (7)$ .

Tap for more steps...

Step 7.2.1.1

Cancel the common factor.

$\frac{x \ln (7)}{\ln (7)} = \frac{\ln (7)}{\ln (7)}$

Step 7.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (7)}{\ln (7)}$

Step 7.3

Simplify the right side.

Tap for more steps...

Step 7.3.1

Cancel the common factor of $\ln (7)$ .

Tap for more steps...

Step 7.3.1.1

Cancel the common factor.

$x = \frac{\ln (7)}{\ln (7)}$

Step 7.3.1.2

Rewrite the expression.

$x = 1$