Basic Math Examples

$12000 = 600 {(1.02317238)}^{z}$

Step 1

Rewrite the equation as $600 \cdot {1.02317238}^{z} = 12000$ .

$600 \cdot {1.02317238}^{z} = 12000$

Step 2

Divide each term in $600 \cdot {1.02317238}^{z} = 12000$ by $600$ and simplify.

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Step 2.1

Divide each term in $600 \cdot {1.02317238}^{z} = 12000$ by $600$ .

$\frac{600 \cdot {1.02317238}^{z}}{600} = \frac{12000}{600}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $600$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{600 \cdot {1.02317238}^{z}}{600} = \frac{12000}{600}$

Step 2.2.1.2

Divide ${1.02317238}^{z}$ by $1$ .

${1.02317238}^{z} = \frac{12000}{600}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $12000$ by $600$ .

${1.02317238}^{z} = 20$

Step 3

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

$\ln ({1.02317238}^{z}) = \ln (20)$

Step 4

Expand $\ln ({1.02317238}^{z})$ by moving $z$ outside the logarithm.

$z \ln (1.02317238) = \ln (20)$

Step 5

Divide each term in $z \ln (1.02317238) = \ln (20)$ by $\ln (1.02317238)$ and simplify.

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Step 5.1

Divide each term in $z \ln (1.02317238) = \ln (20)$ by $\ln (1.02317238)$ .

$\frac{z \ln (1.02317238)}{\ln (1.02317238)} = \frac{\ln (20)}{\ln (1.02317238)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $\ln (1.02317238)$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{z \ln (1.02317238)}{\ln (1.02317238)} = \frac{\ln (20)}{\ln (1.02317238)}$

Step 5.2.1.2

Divide $z$ by $1$ .

$z = \frac{\ln (20)}{\ln (1.02317238)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$z = \frac{\ln (20)}{\ln (1.02317238)}$

Decimal Form:

$z = 130.77239480 \dots$