Solve for x 6400=(8)(2^(4x))

$6400 = (8) (2^{4 x})$

Rewrite the equation as $8 \cdot 2^{4 x} = 6400$ .

$8 \cdot 2^{4 x} = 6400$

Simplify.

Rewrite $8$ as $2^{3}$ .

$2^{3} \cdot 2^{4 x} = 6400$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{3 + 4 x} = 6400$

Divide each term in $2^{3 + 4 x} = 6400$ by $8$ and simplify.

Divide each term in $2^{3 + 4 x} = 6400$ by $8$ .

$\frac{2^{3 + 4 x}}{8} = \frac{6400}{8}$

Simplify the right side.

Divide $6400$ by $8$ .

$\frac{2^{3 + 4 x}}{8} = 800$

Multiply both sides by $8$ .

$\frac{2^{3 + 4 x}}{8} \cdot 8 = 800 \cdot 8$

Simplify.

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{2^{3 + 4 x}}{8} \cdot 8 = 800 \cdot 8$

Rewrite the expression.

$2^{3 + 4 x} = 800 \cdot 8$

Simplify the right side.

Multiply $800$ by $8$ .

$2^{3 + 4 x} = 6400$

Solve for $x$ .

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (2^{3 + 4 x}) = \ln (6400)$

Expand $\ln (2^{3 + 4 x})$ by moving $3 + 4 x$ outside the logarithm.

$(3 + 4 x) \ln (2) = \ln (6400)$

Simplify the left side.

Apply the distributive property.

$3 \ln (2) + 4 x \ln (2) = \ln (6400)$

Reorder $3 \ln (2)$ and $4 x \ln (2)$ .

$4 x \ln (2) + 3 \ln (2) = \ln (6400)$

Move all the terms containing a logarithm to the left side of the equation.

$4 x \ln (2) + 3 \ln (2) - \ln (6400) = 0$

Move all terms not containing $x$ to the right side of the equation.

Subtract $3 \ln (2)$ from both sides of the equation.

$4 x \ln (2) - \ln (6400) = - 3 \ln (2)$

Add $\ln (6400)$ to both sides of the equation.

$4 x \ln (2) = - 3 \ln (2) + \ln (6400)$

Divide each term in $4 x \ln (2) = - 3 \ln (2) + \ln (6400)$ by $4 \ln (2)$ and simplify.

Divide each term in $4 x \ln (2) = - 3 \ln (2) + \ln (6400)$ by $4 \ln (2)$ .

$\frac{4 x \ln (2)}{4 \ln (2)} = \frac{- 3 \ln (2)}{4 \ln (2)} + \frac{\ln (6400)}{4 \ln (2)}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x \ln (2)}{4 \ln (2)} = \frac{- 3 \ln (2)}{4 \ln (2)} + \frac{\ln (6400)}{4 \ln (2)}$

Rewrite the expression.

$\frac{x \ln (2)}{\ln (2)} = \frac{- 3 \ln (2)}{4 \ln (2)} + \frac{\ln (6400)}{4 \ln (2)}$

Cancel the common factor of $\ln (2)$ .

Cancel the common factor.

$\frac{x \ln (2)}{\ln (2)} = \frac{- 3 \ln (2)}{4 \ln (2)} + \frac{\ln (6400)}{4 \ln (2)}$

Divide $x$ by $1$ .

$x = \frac{- 3 \ln (2)}{4 \ln (2)} + \frac{\ln (6400)}{4 \ln (2)}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $\ln (2)$ .

Cancel the common factor.

$x = \frac{- 3 \ln (2)}{4 \ln (2)} + \frac{\ln (6400)}{4 \ln (2)}$

Rewrite the expression.

$x = \frac{- 3}{4} + \frac{\ln (6400)}{4 \ln (2)}$

Move the negative in front of the fraction.

$x = - \frac{3}{4} + \frac{\ln (6400)}{4 \ln (2)}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3}{4} + \frac{\ln (6400)}{4 \ln (2)}$

Decimal Form:

$x = 2.41096404 \dots$

Solve for x 6400=(8)(2^(4x))

Related Questions

Support LCMGCF.com by disabling your adblocker.