Solve for x log of 15- log of 4x=1

$\log (15) - \log (4 x) = 1$

Step 1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log (\frac{15}{4 x}) = 1$

Step 2

Rewrite $\log (\frac{15}{4 x}) = 1$ 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 $b^{y} = x$ .

$10^{1} = \frac{15}{4 x}$

Step 3

Solve for $x$ .

Rewrite the equation as $\frac{15}{4 x} = 10^{1}$ .

$\frac{15}{4 x} = 10$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$4 x, 1$

The LCM of one and any expression is the expression.

$4 x$

Multiply each term in $\frac{15}{4 x} = 10$ by $4 x$ to eliminate the fractions.

Multiply each term in $\frac{15}{4 x} = 10$ by $4 x$ .

$\frac{15}{4 x} (4 x) = 10 (4 x)$

Simplify the left side.

Rewrite using the commutative property of multiplication.

$4 \frac{15}{4 x} x = 10 (4 x)$

Cancel the common factor of $4$ .

Factor $4$ out of $4 x$ .

$4 \frac{15}{4 (x)} x = 10 (4 x)$

Cancel the common factor.

$4 \frac{15}{4 x} x = 10 (4 x)$

Rewrite the expression.

$\frac{15}{x} x = 10 (4 x)$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{15}{x} x = 10 (4 x)$

Rewrite the expression.

$15 = 10 (4 x)$

Simplify the right side.

Multiply $4$ by $10$ .

$15 = 40 x$

Solve the equation.

Rewrite the equation as $40 x = 15$ .

$40 x = 15$

Divide each term in $40 x = 15$ by $40$ and simplify.

Divide each term in $40 x = 15$ by $40$ .

$\frac{40 x}{40} = \frac{15}{40}$

Simplify the left side.

Cancel the common factor of $40$ .

Cancel the common factor.

$\frac{40 x}{40} = \frac{15}{40}$

Divide $x$ by $1$ .

$x = \frac{15}{40}$

Simplify the right side.

Cancel the common factor of $15$ and $40$ .

Factor $5$ out of $15$ .

$x = \frac{5 (3)}{40}$

Cancel the common factors.

Factor $5$ out of $40$ .

$x = \frac{5 \cdot 3}{5 \cdot 8}$

Cancel the common factor.

$x = \frac{5 \cdot 3}{5 \cdot 8}$

Rewrite the expression.

$x = \frac{3}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{8}$

Decimal Form:

$x = 0.375$

Solve for x log of 15- log of 4x=1

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