Precalculus Examples

$x \cdot \log (5) + x \cdot \log (7) = \log (9)$

Step 1

Simplify the left side.

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Step 1.1

Multiply $x$ by $\log (7)$ .

$x \log (5) + x \log (7) = \log (9)$

Step 2

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

$x \log (5) + x \log (7) - \log (9) = 0$

Step 3

Add $\log (9)$ to both sides of the equation.

$x \log (5) + x \log (7) = \log (9)$

Step 4

Factor $x$ out of $x \log (5) + x \log (7)$ .

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Step 4.1

Factor $x$ out of $x \log (5)$ .

$x (\log (5)) + x \log (7) = \log (9)$

Step 4.2

Factor $x$ out of $x \log (7)$ .

$x (\log (5)) + x (\log (7)) = \log (9)$

Step 4.3

Factor $x$ out of $x (\log (5)) + x (\log (7))$ .

$x (\log (5) + \log (7)) = \log (9)$

Step 5

Divide each term in $x (\log (5) + \log (7)) = \log (9)$ by $\log (5) + \log (7)$ and simplify.

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Step 5.1

Divide each term in $x (\log (5) + \log (7)) = \log (9)$ by $\log (5) + \log (7)$ .

$\frac{x (\log (5) + \log (7))}{\log (5) + \log (7)} = \frac{\log (9)}{\log (5) + \log (7)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $\log (5) + \log (7)$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{x (\log (5) + \log (7))}{\log (5) + \log (7)} = \frac{\log (9)}{\log (5) + \log (7)}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\log (9)}{\log (5) + \log (7)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\log (9)}{\log (5) + \log (7)}$

Decimal Form:

$x = 0.61800547 \dots$