Solve for x log of 5x-4=3

$\log (5 x - 4) = 3$

Step 1

Rewrite $\log (5 x - 4) = 3$ 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 $b^{y} = x$ .

$10^{3} = 5 x - 4$

Step 2

Solve for $x$ .

Rewrite the equation as $5 x - 4 = 10^{3}$ .

$5 x - 4 = 10^{3}$

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

$5 x - 4 = 1000$

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

Add $4$ to both sides of the equation.

$5 x = 1000 + 4$

Add $1000$ and $4$ .

$5 x = 1004$

Divide each term in $5 x = 1004$ by $5$ and simplify.

Divide each term in $5 x = 1004$ by $5$ .

$\frac{5 x}{5} = \frac{1004}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{1004}{5}$

Divide $x$ by $1$ .

$x = \frac{1004}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1004}{5}$

Decimal Form:

$x = 200.8$

Mixed Number Form:

$x = 200 \frac{4}{5}$

Solve for x log of 5x-4=3

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