Finite Math Examples

$10^{2 x - 1} = 0.25$

Step 1

Take the base $10$ logarithm of both sides of the equation to remove the variable from the exponent.

$\log (10^{2 x - 1}) = \log (0.25)$

Step 2

Expand the left side.

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Step 2.1

Expand $\log (10^{2 x - 1})$ by moving $2 x - 1$ outside the logarithm.

$(2 x - 1) \log (10) = \log (0.25)$

Step 2.2

Logarithm base $10$ of $10$ is $1$ .

$(2 x - 1) \cdot 1 = \log (0.25)$

Step 2.3

Multiply $2 x - 1$ by $1$ .

$2 x - 1 = \log (0.25)$

Step 3

Simplify the right side.

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Step 3.1

Log base $10$ of $0.25$ is approximately $- 0.60205999$ .

$2 x - 1 = - 0.60205999$

Step 4

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

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Step 4.1

Add $1$ to both sides of the equation.

$2 x = - 0.60205999 + 1$

Step 4.2

Add $- 0.60205999$ and $1$ .

$2 x = 0.39794$

Step 5

Divide each term in $2 x = 0.39794$ by $2$ and simplify.

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Step 5.1

Divide each term in $2 x = 0.39794$ by $2$ .

$\frac{2 x}{2} = \frac{0.39794}{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{0.39794}{2}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{0.39794}{2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $0.39794$ by $2$ .

$x = 0.19897$