Solve for x 10^(x+2)-12=22

$10^{x + 2} - 12 = 22$

Step 1

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

Add $12$ to both sides of the equation.

$10^{x + 2} = 22 + 12$

Add $22$ and $12$ .

$10^{x + 2} = 34$

Step 2

Take the base $10$ logarithm of both sides of the equation to remove the variable from the exponent.

$\log (10^{x + 2}) = \log (34)$

Step 3

Expand the left side.

Expand $\log (10^{x + 2})$ by moving $x + 2$ outside the logarithm.

$(x + 2) \log (10) = \log (34)$

Logarithm base $10$ of $10$ is $1$ .

$(x + 2) \cdot 1 = \log (34)$

Multiply $x + 2$ by $1$ .

$x + 2 = \log (34)$

Step 4

Subtract $2$ from both sides of the equation.

$x = \log (34) - 2$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \log (34) - 2$

Decimal Form:

$x = - 0.46852108 \dots$