Trigonometry Examples

$\log (2 t - 4) = \log (14 - 3 t)$

Step 1

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$2 t - 4 = 14 - 3 t$

Step 2

Solve for $t$ .

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Step 2.1

Move all terms containing $t$ to the left side of the equation.

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Step 2.1.1

Add $3 t$ to both sides of the equation.

$2 t - 4 + 3 t = 14$

Step 2.1.2

Add $2 t$ and $3 t$ .

$5 t - 4 = 14$

Step 2.2

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

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Step 2.2.1

Add $4$ to both sides of the equation.

$5 t = 14 + 4$

Step 2.2.2

Add $14$ and $4$ .

$5 t = 18$

Step 2.3

Divide each term in $5 t = 18$ by $5$ and simplify.

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Step 2.3.1

Divide each term in $5 t = 18$ by $5$ .

$\frac{5 t}{5} = \frac{18}{5}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $5$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{5 t}{5} = \frac{18}{5}$

Step 2.3.2.1.2

Divide $t$ by $1$ .

$t = \frac{18}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$t = \frac{18}{5}$

Decimal Form:

$t = 3.6$

Mixed Number Form:

$t = 3 \frac{3}{5}$