Solve 16^(2x 1)=4^(3x^3)

Question

Solve the equation

Solve for x

x_{1} = - \frac{2 3}{3}, x_{2} = 0, x_{3} = \frac{2 3}{3}

Alternative Form

x_{1} \approx - 1.154701, x_{2} = 0, x_{3} \approx 1.154701

Evaluate

1 6^{2 x \times 1} = 4^{3 x^{3}}

Multiply the terms

1 6^{2 x} = 4^{3 x^{3}}

Rewrite the expression

More Steps

Evaluate

1 6^{2 x}

Write the number in exponential form with the base of 4

(4^{2})^{2 x}

Rewrite the expression

4^{4 x}

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

Since the bases are the same,set the exponents equal

4 x = 3 x^{3}

Add or subtract both sides

4 x - 3 x^{3} = 0

Factor the expression

x (4 - 3 x^{2}) = 0

Separate the equation into 2 possible cases

x = 0 4 - 3 x^{2} = 0

Solve the equation

More Steps

Evaluate

4 - 3 x^{2} = 0

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

- 3 x^{2} = 0 - 4

Removing 0 doesn't change the value,so remove it from the expression

- 3 x^{2} = - 4

Change the signs on both sides of the equation

3 x^{2} = 4

Divide both sides

\frac{3 x ^{2}}{3} = \frac{4}{3}

Divide the numbers

x^{2} = \frac{4}{3}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{4}{3}

Simplify the expression

More Steps

Evaluate

\frac{4}{3}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4}{3}

Simplify the radical expression

\frac{2}{3}

Multiply by the Conjugate

\frac{2 3}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{2 3}{3}

x = \pm \frac{2 3}{3}

Separate the equation into 2 possible cases

x = \frac{2 3}{3} x = - \frac{2 3}{3}

x = 0 x = \frac{2 3}{3} x = - \frac{2 3}{3}

Solution

x_{1} = - \frac{2 3}{3}, x_{2} = 0, x_{3} = \frac{2 3}{3}

Alternative Form

x_{1} \approx - 1.154701, x_{2} = 0, x_{3} \approx 1.154701

Show Solution