Precalculus Examples

$2700 = 300 \cdot 2^{10 x}$

Step 1

Rewrite the equation as $300 \cdot 2^{10 x} = 2700$ .

$300 \cdot 2^{10 x} = 2700$

Step 2

Divide each term in $300 \cdot 2^{10 x} = 2700$ by $300$ and simplify.

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Step 2.1

Divide each term in $300 \cdot 2^{10 x} = 2700$ by $300$ .

$\frac{300 \cdot 2^{10 x}}{300} = \frac{2700}{300}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $300$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{300 \cdot 2^{10 x}}{300} = \frac{2700}{300}$

Step 2.2.1.2

Divide $2^{10 x}$ by $1$ .

$2^{10 x} = \frac{2700}{300}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $2700$ by $300$ .

$2^{10 x} = 9$

Step 3

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

$\ln (2^{10 x}) = \ln (9)$

Step 4

Expand $\ln (2^{10 x})$ by moving $10 x$ outside the logarithm.

$10 x \ln (2) = \ln (9)$

Step 5

Divide each term in $10 x \ln (2) = \ln (9)$ by $10 \ln (2)$ and simplify.

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Step 5.1

Divide each term in $10 x \ln (2) = \ln (9)$ by $10 \ln (2)$ .

$\frac{10 x \ln (2)}{10 \ln (2)} = \frac{\ln (9)}{10 \ln (2)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $10$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{10 x \ln (2)}{10 \ln (2)} = \frac{\ln (9)}{10 \ln (2)}$

Step 5.2.1.2

Rewrite the expression.

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (9)}{10 \ln (2)}$

Step 5.2.2

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

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Step 5.2.2.1

Cancel the common factor.

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (9)}{10 \ln (2)}$

Step 5.2.2.2

Divide $x$ by $1$ .

$x = \frac{\ln (9)}{10 \ln (2)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (9)}{10 \ln (2)}$

Decimal Form:

$x = 0.31699250 \dots$