\text{Solve for }x of 5^x=4^{(x+3)}

x=\frac{6}{\log_{2}{\left(5\right)}-2}

Solve 5^x=4^(x+3)

Evaluate

5^{x} = 4^{(x + 3)}

Remove the parentheses

5^{x} = 4^{x + 3}

Take the logarithm of both sides

lo g_{4} (5^{x}) = lo g_{4} (4^{x + 3})

Evaluate the logarithm

\frac{x}{2} lo g_{2} (5) = \frac{2 ( x + 3 )}{2}

Rewrite the expression

\frac{x lo g _{2} ( 5 )}{2} = \frac{2 ( x + 3 )}{2}

Multiply both sides of the equation by LCD

\frac{x lo g _{2} ( 5 )}{2} \times 2 = \frac{2 ( x + 3 )}{2} \times 2

Simplify the equation

More Steps

lo g_{2} (5) \times x = \frac{2 ( x + 3 )}{2} \times 2

Simplify the equation

More Steps

lo g_{2} (5) \times x = 2 x + 6

Move the variable to the left side

lo g_{2} (5) \times x - 2 x = 6

Collect like terms by calculating the sum or difference of their coefficients

(lo g_{2} (5) - 2) x = 6

Divide both sides

\frac{( lo g _{2} ( 5 ) - 2 ) x}{lo g _{2} ( 5 ) - 2} = \frac{6}{lo g _{2} ( 5 ) - 2}

Solution

x = \frac{6}{lo g _{2} ( 5 ) - 2}

Alternative Form

x \approx 18.637702