Solve for x log base 4 of x+1- log base 4 of x=3

$\log_{4} (x + 1) - \log_{4} (x) = 3$

Step 1

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

$\log_{4} (\frac{x + 1}{x}) = 3$

Step 2

Rewrite $\log_{4} (\frac{x + 1}{x}) = 3$ 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 $b^{y} = x$ .

$4^{3} = \frac{x + 1}{x}$

Step 3

Cross multiply to remove the fraction.

$x + 1 = 4^{3} (x)$

Step 4

Raise $4$ to the power of $3$ .

$x + 1 = 64 x$

Step 5

Move all terms containing $x$ to the left side of the equation.

Subtract $64 x$ from both sides of the equation.

$x + 1 - 64 x = 0$

Subtract $64 x$ from $x$ .

$- 63 x + 1 = 0$

Step 6

Subtract $1$ from both sides of the equation.

$- 63 x = - 1$

Step 7

Divide each term in $- 63 x = - 1$ by $- 63$ and simplify.

Divide each term in $- 63 x = - 1$ by $- 63$ .

$\frac{- 63 x}{- 63} = \frac{- 1}{- 63}$

Simplify the left side.

Cancel the common factor of $- 63$ .

Cancel the common factor.

$\frac{- 63 x}{- 63} = \frac{- 1}{- 63}$

Divide $x$ by $1$ .

$x = \frac{- 1}{- 63}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{1}{63}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{63}$

Decimal Form:

$x = 0.\overline{015873}$

Solve for x log base 4 of x+1- log base 4 of x=3

Related Questions

Support LCMGCF.com by disabling your adblocker.