Precalculus Examples

$5 (10^{x - 6}) = 7$

Step 1

Divide each term in $5 \cdot 10^{x - 6} = 7$ by $5$ and simplify.

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Step 1.1

Divide each term in $5 \cdot 10^{x - 6} = 7$ by $5$ .

$\frac{5 \cdot 10^{x - 6}}{5} = \frac{7}{5}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $5$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{5 \cdot 10^{x - 6}}{5} = \frac{7}{5}$

Step 1.2.1.2

Divide $10^{x - 6}$ by $1$ .

$10^{x - 6} = \frac{7}{5}$

Step 2

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

$\log (10^{x - 6}) = \log (\frac{7}{5})$

Step 3

Expand the left side.

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Step 3.1

Expand $\log (10^{x - 6})$ by moving $x - 6$ outside the logarithm.

$(x - 6) \log (10) = \log (\frac{7}{5})$

Step 3.2

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

$(x - 6) \cdot 1 = \log (\frac{7}{5})$

Step 3.3

Multiply $x - 6$ by $1$ .

$x - 6 = \log (\frac{7}{5})$

Step 4

Add $6$ to both sides of the equation.

$x = \log (\frac{7}{5}) + 6$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \log (\frac{7}{5}) + 6$

Decimal Form:

$x = 6.14612803 \dots$