Basic Math Examples

$5 \cdot 6^{m + 7} + 8.5 = 97$

Step 1

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

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Step 1.1

Subtract $8.5$ from both sides of the equation.

$5 \cdot 6^{m + 7} = 97 - 8.5$

Step 1.2

Subtract $8.5$ from $97$ .

$5 \cdot 6^{m + 7} = 88.5$

Step 2

Divide each term in $5 \cdot 6^{m + 7} = 88.5$ by $5$ and simplify.

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Step 2.1

Divide each term in $5 \cdot 6^{m + 7} = 88.5$ by $5$ .

$\frac{5 \cdot 6^{m + 7}}{5} = \frac{88.5}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5 \cdot 6^{m + 7}}{5} = \frac{88.5}{5}$

Step 2.2.1.2

Divide $6^{m + 7}$ by $1$ .

$6^{m + 7} = \frac{88.5}{5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $88.5$ by $5$ .

$6^{m + 7} = 17.7$

Step 3

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

$\ln (6^{m + 7}) = \ln (17.7)$

Step 4

Expand $\ln (6^{m + 7})$ by moving $m + 7$ outside the logarithm.

$(m + 7) \ln (6) = \ln (17.7)$

Step 5

Simplify the left side.

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Step 5.1

Apply the distributive property.

$m \ln (6) + 7 \ln (6) = \ln (17.7)$

Step 6

Move all the terms containing a logarithm to the left side of the equation.

$m \ln (6) + 7 \ln (6) - \ln (17.7) = 0$

Step 7

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

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Step 7.1

Subtract $7 \ln (6)$ from both sides of the equation.

$m \ln (6) - \ln (17.7) = - 7 \ln (6)$

Step 7.2

Add $\ln (17.7)$ to both sides of the equation.

$m \ln (6) = - 7 \ln (6) + \ln (17.7)$

Step 8

Divide each term in $m \ln (6) = - 7 \ln (6) + \ln (17.7)$ by $\ln (6)$ and simplify.

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Step 8.1

Divide each term in $m \ln (6) = - 7 \ln (6) + \ln (17.7)$ by $\ln (6)$ .

$\frac{m \ln (6)}{\ln (6)} = \frac{- 7 \ln (6)}{\ln (6)} + \frac{\ln (17.7)}{\ln (6)}$

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.

$\frac{m \ln (6)}{\ln (6)} = \frac{- 7 \ln (6)}{\ln (6)} + \frac{\ln (17.7)}{\ln (6)}$

Step 8.2.1.2

Divide $m$ by $1$ .

$m = \frac{- 7 \ln (6)}{\ln (6)} + \frac{\ln (17.7)}{\ln (6)}$

Step 8.3

Simplify the right side.

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Step 8.3.1

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

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Step 8.3.1.1

Cancel the common factor.

$m = \frac{- 7 \ln (6)}{\ln (6)} + \frac{\ln (17.7)}{\ln (6)}$

Step 8.3.1.2

Divide $- 7$ by $1$ .

$m = - 7 + \frac{\ln (17.7)}{\ln (6)}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$m = - 7 + \frac{\ln (17.7)}{\ln (6)}$

Decimal Form:

$m = - 5.39623303 \dots$