Solve for x log base 125 of 25=x

$\log_{125} (25) = x$

Step 1

Rewrite the equation as $x = \log_{125} (25)$ .

$x = \log_{125} (25)$

Step 2

Logarithm base $125$ of $25$ is $\frac{2}{3}$ .

Rewrite as an equation.

$x = \log_{125} (25) = x$

Rewrite $\log_{125} (25) = x$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b$ does not equal $1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$x = 125^{x} = 25$

Create expressions in the equation that all have equal bases.

$x = {(5^{3})}^{x} = 5^{2}$

Rewrite ${(5^{3})}^{x}$ as $5^{3 x}$ .

$x = 5^{3 x} = 5^{2}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x = 3 x = 2$

Solve for $x$ .

$x = x = \frac{2}{3}$

The variable $x$ is equal to $\frac{2}{3}$ .

$x = \frac{2}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{3}$

Decimal Form:

$x = 0.\overline{6}$

Solve for x log base 125 of 25=x

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