Solve 27^(x^3) = 9^(3x^4)

Evaluate

2 7^{(x^{3})} = 9^{3 x^{4}}

Rewrite the expression

More Steps

3^{3 x^{3}} = 9^{3 x^{4}}

Rewrite the expression

More Steps

3^{3 x^{3}} = 3^{6 x^{4}}

Since the bases are the same,set the exponents equal

3 x^{3} = 6 x^{4}

Add or subtract both sides

3 x^{3} - 6 x^{4} = 0

Factor the expression

3 x^{3} (1 - 2 x) = 0

Divide both sides

x^{3} (1 - 2 x) = 0

Separate the equation into 2 possible cases

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

The only way a power can be 0 is when the base equals 0

x = 0 1 - 2 x = 0

Solve the equation

More Steps

x = 0 x = \frac{1}{2}

Solution

x_{1} = 0, x_{2} = \frac{1}{2}

Alternative Form

x_{1} = 0, x_{2} = 0.5

Solve the equation