Basic Math Examples

6400 = 2^{x}

$6400 = 2^{x}$

Step 1

Since

x

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

2^{x} = 6400

$2^{x} = 6400$

Step 2

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

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

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

Step 3

Expand

ln (2^{x})

$\ln (2^{x})$ by moving

x

$x$ outside the logarithm.

x ln (2) = ln (6400)

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

Step 4

Divide each term in

x ln (2) = ln (6400)

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

ln (2)

$\ln (2)$ and simplify.

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Step 4.1

Divide each term in

x ln (2) = ln (6400)

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

ln (2)

$\ln (2)$ .

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

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of

ln (2)

$\ln (2)$ .

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Step 4.2.1.1

Cancel the common factor.

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

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

Step 4.2.1.2

Divide

x

$x$ by

1

$1$ .

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