Solve log x^32 = 5

Evaluate

lo g_{10} (x^{3} \times 2) = 5

Find the domain

More Steps

lo g_{10} (x^{3} \times 2) = 5, x > 0

Use the commutative property to reorder the terms

lo g_{10} (2 x^{3}) = 5

Convert the logarithm into exponential form using the fact that lo g_{a} x = b is equal to x = a^{b}

2 x^{3} = 1 0^{5}

Divide both sides

\frac{2 x ^{3}}{2} = \frac{1 0 ^{5}}{2}

Divide the numbers

x^{3} = \frac{1 0 ^{5}}{2}

Divide the numbers

More Steps

x^{3} = 50000

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

3 x^{3} = 350000

Calculate

x = 350000

Simplify the root

More Steps

x = 10350

Check if the solution is in the defined range

x = 10350, x > 0

Solution

x = 10350

Alternative Form

x \approx 36.840315

Solve the equation