Precalculus Examples

$5 \log (x + 2) = \log (5^{4})$

Step 1

Simplify $5 \log (x + 2)$ by moving $5$ inside the logarithm.

$\log ({(x + 2)}^{5}) = \log (5^{4})$

Step 2

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

${(x + 2)}^{5} = 5^{4}$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x + 2 = \sqrt[5]{5^{4}}$

Step 3.2

Raise $5$ to the power of $4$ .

$x + 2 = \sqrt[5]{625}$

Step 3.3

Subtract $2$ from both sides of the equation.

$x = \sqrt[5]{625} - 2$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt[5]{625} - 2$

Decimal Form:

$x = 1.62389831 \dots$