Algebra Examples

$6^{x + 3} - 6^{x} = 215$

Step 1

Factor out $6^{x}$ from the expression.

$6^{x} (216 - 1)$

Step 2

Subtract $1$ from $216$ .

$6^{x} \cdot 215 = 215$

Step 3

Move $215$ to the left of $6^{x}$ .

$215 \cdot 6^{x} = 215$

Step 4

Divide each term in $215 \cdot 6^{x} = 215$ by $215$ and simplify.

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Step 4.1

Divide each term in $215 \cdot 6^{x} = 215$ by $215$ .

$\frac{215 \cdot 6^{x}}{215} = \frac{215}{215}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $215$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{215 \cdot 6^{x}}{215} = \frac{215}{215}$

Step 4.2.1.2

Divide $6^{x}$ by $1$ .

$6^{x} = \frac{215}{215}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $215$ by $215$ .

$6^{x} = 1$

Step 5

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

$\ln (6^{x}) = \ln (1)$

Step 6

Expand $\ln (6^{x})$ by moving $x$ outside the logarithm.

$x \ln (6) = \ln (1)$

Step 7

Simplify the right side.

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Step 7.1

The natural logarithm of $1$ is $0$ .

$x \ln (6) = 0$

Step 8

Divide each term in $x \ln (6) = 0$ by $\ln (6)$ and simplify.

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Step 8.1

Divide each term in $x \ln (6) = 0$ by $\ln (6)$ .

$\frac{x \ln (6)}{\ln (6)} = \frac{0}{\ln (6)}$

Step 8.2

Simplify the left side.

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Step 8.2.1

Cancel the common factor of $\ln (6)$ .

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Step 8.2.1.1

Cancel the common factor.

$\frac{x \ln (6)}{\ln (6)} = \frac{0}{\ln (6)}$

Step 8.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{\ln (6)}$

Step 8.3

Simplify the right side.

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Step 8.3.1

Divide $0$ by $\ln (6)$ .

$x = 0$