Solve for x 2^x=10

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Algebra

Solve for x 2^x=10

$2^{x} = 10$

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

$\ln (2^{x}) = \ln (10)$

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

$x \ln (2) = \ln (10)$

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

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Divide each term in $x \ln (2) = \ln (10)$ by $\ln (2)$ .

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (10)}{\ln (2)}$

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

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Cancel the common factor.

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (10)}{\ln (2)}$

Divide $x$ by $1$ .

$x = \frac{\ln (10)}{\ln (2)}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (10)}{\ln (2)}$

Decimal Form:

$x = 3.32192809 \dots$

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