Precalculus Examples

$12 = 10^{x + 3} - 9$

Step 1

Rewrite the equation as $10^{x + 3} - 9 = 12$ .

$10^{x + 3} - 9 = 12$

Step 2

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

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Step 2.1

Add $9$ to both sides of the equation.

$10^{x + 3} = 12 + 9$

Step 2.2

Add $12$ and $9$ .

$10^{x + 3} = 21$

Step 3

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

$\log (10^{x + 3}) = \log (21)$

Step 4

Expand the left side.

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Step 4.1

Expand $\log (10^{x + 3})$ by moving $x + 3$ outside the logarithm.

$(x + 3) \log (10) = \log (21)$

Step 4.2

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

$(x + 3) \cdot 1 = \log (21)$

Step 4.3

Multiply $x + 3$ by $1$ .

$x + 3 = \log (21)$

Step 5

Subtract $3$ from both sides of the equation.

$x = \log (21) - 3$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \log (21) - 3$

Decimal Form:

$x = - 1.67778070 \dots$