Solve for x 7 log base 5 of x-3=15

$7 \log_{5} (x) - 3 = 15$

Move all terms not containing $\log_{5} (x)$ to the right side of the equation.

Add $3$ to both sides of the equation.

$7 \log_{5} (x) = 15 + 3$

Add $15$ and $3$ .

$7 \log_{5} (x) = 18$

Divide each term in $7 \log_{5} (x) = 18$ by $7$ and simplify.

Divide each term in $7 \log_{5} (x) = 18$ by $7$ .

$\frac{7 \log_{5} (x)}{7} = \frac{18}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 \log_{5} (x)}{7} = \frac{18}{7}$

Divide $\log_{5} (x)$ by $1$ .

$\log_{5} (x) = \frac{18}{7}$

Rewrite $\log_{5} (x) = \frac{18}{7}$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$5^{\frac{18}{7}} = x$

Rewrite the equation as $x = 5^{\frac{18}{7}}$ .

$x = 5^{\frac{18}{7}}$

The result can be shown in multiple forms.

Exact Form:

$x = 5^{\frac{18}{7}}$

Decimal Form:

$x = 62.71211382 \dots$

Solve for x 7 log base 5 of x-3=15

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