Solve ( 1/32 )^(4x^2)=128^(x 7)

Evaluate

(\frac{1}{32})^{4 x^{2}} = 12 8^{x \times 7}

Use the commutative property to reorder the terms

(\frac{1}{32})^{4 x^{2}} = 12 8^{7 x}

Rewrite the expression

More Steps

2^{- 20 x^{2}} = 12 8^{7 x}

Rewrite the expression

More Steps

2^{- 20 x^{2}} = 2^{49 x}

Since the bases are the same,set the exponents equal

- 20 x^{2} = 49 x

Add or subtract both sides

- 20 x^{2} - 49 x = 0

Factor the expression

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- x (20 x + 49) = 0

When the product of factors equals 0,at least one factor is 0

- x = 0 20 x + 49 = 0

Solve the equation for x

x = 0 20 x + 49 = 0

Solve the equation for x

More Steps

x = 0 x = - \frac{49}{20}

Solution

x_{1} = - \frac{49}{20}, x_{2} = 0

Alternative Form

x_{1} = - 2.45, x_{2} = 0

Solve the equation