Basic Math Examples

$\log (25) = 22 \log (2 F)$

Step 1

Rewrite the equation as $22 \log (2 F) = \log (25)$ .

$22 \log (2 F) = \log (25)$

Step 2

Simplify $22 \log (2 F)$ by moving $22$ inside the logarithm.

$\log ({(2 F)}^{22}) = \log (25)$

Step 3

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

${(2 F)}^{22} = 25$

Step 4

Solve for $F$ .

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Step 4.1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$2 F = \pm \sqrt[22]{25}$

Step 4.2

Simplify $\pm \sqrt[22]{25}$ .

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Step 4.2.1

Rewrite $25$ as $5^{2}$ .

$2 F = \pm \sqrt[22]{5^{2}}$

Step 4.2.2

Rewrite $\sqrt[22]{5^{2}}$ as $\sqrt[11]{\sqrt{5^{2}}}$ .

$2 F = \pm \sqrt[11]{\sqrt{5^{2}}}$

Step 4.2.3

Pull terms out from under the radical, assuming positive real numbers.

$2 F = \pm \sqrt[11]{5}$

Step 4.3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.3.1

First, use the positive value of the $\pm$ to find the first solution.

$2 F = \sqrt[11]{5}$

Step 4.3.2

Divide each term in $2 F = \sqrt[11]{5}$ by $2$ and simplify.

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Step 4.3.2.1

Divide each term in $2 F = \sqrt[11]{5}$ by $2$ .

$\frac{2 F}{2} = \frac{\sqrt[11]{5}}{2}$

Step 4.3.2.2

Simplify the left side.

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Step 4.3.2.2.1

Cancel the common factor of $2$ .

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Step 4.3.2.2.1.1

Cancel the common factor.

$\frac{2 F}{2} = \frac{\sqrt[11]{5}}{2}$

Step 4.3.2.2.1.2

Divide $F$ by $1$ .

$F = \frac{\sqrt[11]{5}}{2}$

Step 4.3.3

Next, use the negative value of the $\pm$ to find the second solution.

$2 F = - \sqrt[11]{5}$

Step 4.3.4

Divide each term in $2 F = - \sqrt[11]{5}$ by $2$ and simplify.

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Step 4.3.4.1

Divide each term in $2 F = - \sqrt[11]{5}$ by $2$ .

$\frac{2 F}{2} = \frac{- \sqrt[11]{5}}{2}$

Step 4.3.4.2

Simplify the left side.

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Step 4.3.4.2.1

Cancel the common factor of $2$ .

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Step 4.3.4.2.1.1

Cancel the common factor.

$\frac{2 F}{2} = \frac{- \sqrt[11]{5}}{2}$

Step 4.3.4.2.1.2

Divide $F$ by $1$ .

$F = \frac{- \sqrt[11]{5}}{2}$

Step 4.3.4.3

Simplify the right side.

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Step 4.3.4.3.1

Move the negative in front of the fraction.

$F = - \frac{\sqrt[11]{5}}{2}$

Step 4.3.5

The complete solution is the result of both the positive and negative portions of the solution.

$F = \frac{\sqrt[11]{5}}{2}, - \frac{\sqrt[11]{5}}{2}$

Step 5

Exclude the solutions that do not make $\log (25) = 22 \log (2 F)$ true.

$F = \frac{\sqrt[11]{5}}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$F = \frac{\sqrt[11]{5}}{2}$

Decimal Form:

$F = 0.57877895 \dots$