Trigonometry Examples

$2 {\log_{5}}^{2} (t) - 3 \log_{5} (t) = 2$

Step 1

Simplify $- 3 \log_{5} (t)$ by moving $3$ inside the logarithm.

$2 {\log_{5}}^{2} (t) - \log_{5} (t^{3}) = 2$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$t \approx \frac{\sqrt{5}}{5}, 25$

Step 3

The result can be shown in multiple forms.

Exact Form:

$t \approx \frac{\sqrt{5}}{5}, 25$

Decimal Form:

$t \approx 0.44721359 \dots, 25$

Step 4