Solve for y 6400=2^x

$6400 = 2^{x}$

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$2^{x} = 6400$

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

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

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

$x \ln (2) = \ln (6400)$

Divide each term by $\ln (2)$ and simplify.

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Divide each term in $x \ln (2) = \ln (6400)$ by $\ln (2)$ .

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (6400)}{\ln (2)}$

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

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Cancel the common factor.

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (6400)}{\ln (2)}$

Divide $x$ by $1$ .

$x = \frac{\ln (6400)}{\ln (2)}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (6400)}{\ln (2)}$

Decimal Form:

$x = 12.64385618 \dots$

Solve for y 6400=2^x

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