Solve for x log of 2x+5=3

$\log (2 x + 5) = 3$

Rewrite $\log (2 x + 5) = 3$ 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 $b^{y} = x$ .

$10^{3} = 2 x + 5$

Solve for $x$ .

Rewrite the equation as $2 x + 5 = 10^{3}$ .

$2 x + 5 = 10^{3}$

Raise $10$ to the power of $3$ .

$2 x + 5 = 1000$

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

Subtract $5$ from both sides of the equation.

$2 x = 1000 - 5$

Subtract $5$ from $1000$ .

$2 x = 995$

Divide each term in $2 x = 995$ by $2$ and simplify.

Divide each term in $2 x = 995$ by $2$ .

$\frac{2 x}{2} = \frac{995}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{995}{2}$

Divide $x$ by $1$ .

$x = \frac{995}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{995}{2}$

Decimal Form:

$x = 497.5$

Mixed Number Form:

$x = 497 \frac{1}{2}$

Solve for x log of 2x+5=3

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