Trigonometry Examples

$\log_{5} (7^{x + 3}) = 16$

Step 1

Expand $\log_{5} (7^{x + 3})$ by moving $x + 3$ outside the logarithm.

$(x + 3) \log_{5} (7)$

Step 2

The expanded equation is $(x + 3) \log_{5} (7) = 16$ .

$(x + 3) \log_{5} (7) = 16$

Step 3

Divide each term in $(x + 3) \log_{5} (7) = 16$ by $\log_{5} (7)$ and simplify.

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Step 3.1

Divide each term in $(x + 3) \log_{5} (7) = 16$ by $\log_{5} (7)$ .

$\frac{(x + 3) \log_{5} (7)}{\log_{5} (7)} = \frac{16}{\log_{5} (7)}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $\log_{5} (7)$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{(x + 3) \log_{5} (7)}{\log_{5} (7)} = \frac{16}{\log_{5} (7)}$

Step 3.2.1.2

Divide $x + 3$ by $1$ .

$x + 3 = \frac{16}{\log_{5} (7)}$

Step 4

Subtract $3$ from both sides of the equation.

$x = \frac{16}{\log_{5} (7)} - 3$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{16}{\log_{5} (7)} - 3$

Decimal Form:

$x = 10.23339960 \dots$