Solve 625*5^(3x^3) = 125

Evaluate

625 \times 5^{3 x^{3}} = 125

Multiply the terms

More Steps

5^{3 x^{3} + 4} = 125

Rewrite in exponential form

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

Since the bases are the same,set the exponents equal

3 x^{3} + 4 = 3

Move the constant to the right-hand side and change its sign

3 x^{3} = 3 - 4

Subtract the numbers

3 x^{3} = - 1

Divide both sides

\frac{3 x ^{3}}{3} = \frac{- 1}{3}

Divide the numbers

x^{3} = \frac{- 1}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x^{3} = - \frac{1}{3}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 - \frac{1}{3}

Calculate

x = 3 - \frac{1}{3}

Solution

More Steps

x = - \frac{3 9}{3}

Alternative Form

x \approx - 0.693361

Solve the equation