Solve for x 240=7930(0.93)^(4x)-340

$240 = 7930 {(0.93)}^{4 x} - 340$

Step 1

Rewrite the equation as $7930 \cdot {0.93}^{4 x} - 340 = 240$ .

$7930 \cdot {0.93}^{4 x} - 340 = 240$

Step 2

Move all terms not containing $x$ to the right side of the equation.

Add $340$ to both sides of the equation.

$7930 \cdot {0.93}^{4 x} = 240 + 340$

Add $240$ and $340$ .

$7930 \cdot {0.93}^{4 x} = 580$

Step 3

Divide each term in $(7930 \cdot {0.93}^{4 x}) = 580$ by $7930$ and simplify.

Divide each term in $(7930 \cdot {0.93}^{4 x}) = 580$ by $7930$ .

$\frac{(7930 \cdot {0.93}^{4 x})}{7930} = \frac{580}{7930}$

Simplify the left side.

Cancel the common factor of $7930$ .

Cancel the common factor.

$\frac{7930 \cdot {0.93}^{4 x}}{7930} = \frac{580}{7930}$

Divide ${0.93}^{4 x}$ by $1$ .

${0.93}^{4 x} = \frac{580}{7930}$

Simplify the right side.

Cancel the common factor of $580$ and $7930$ .

Factor $10$ out of $580$ .

${0.93}^{4 x} = \frac{10 (58)}{7930}$

Cancel the common factors.

Factor $10$ out of $7930$ .

${0.93}^{4 x} = \frac{10 \cdot 58}{10 \cdot 793}$

Cancel the common factor.

${0.93}^{4 x} = \frac{10 \cdot 58}{10 \cdot 793}$

Rewrite the expression.

${0.93}^{4 x} = \frac{58}{793}$

Step 4

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

$\ln ({0.93}^{4 x}) = \ln (\frac{58}{793})$

Step 5

Expand $\ln ({0.93}^{4 x})$ by moving $4 x$ outside the logarithm.

$4 x \ln (0.93) = \ln (\frac{58}{793})$

Step 6

Divide each term in $4 x \ln (0.93) = \ln (\frac{58}{793})$ by $4 \ln (0.93)$ and simplify.

Divide each term in $4 x \ln (0.93) = \ln (\frac{58}{793})$ by $4 \ln (0.93)$ .

$\frac{4 x \ln (0.93)}{4 \ln (0.93)} = \frac{\ln (\frac{58}{793})}{4 \ln (0.93)}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x \ln (0.93)}{4 \ln (0.93)} = \frac{\ln (\frac{58}{793})}{4 \ln (0.93)}$

Rewrite the expression.

$\frac{x \ln (0.93)}{\ln (0.93)} = \frac{\ln (\frac{58}{793})}{4 \ln (0.93)}$

Cancel the common factor of $\ln (0.93)$ .

Cancel the common factor.

$\frac{x \ln (0.93)}{\ln (0.93)} = \frac{\ln (\frac{58}{793})}{4 \ln (0.93)}$

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{58}{793})}{4 \ln (0.93)}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (\frac{58}{793})}{4 \ln (0.93)}$

Decimal Form:

$x = 9.00976726 \dots$

Solve for x 240=7930(0.93)^(4x)-340

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