Algebra Examples

$\log_{3} (4) + \log_{3} (y) + \frac{1}{2} \cdot \log_{3} (49)$

Step 1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{3} (4 y) + \frac{1}{2} \cdot \log_{3} (49)$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Simplify $\frac{1}{2} \log_{3} (49)$ by moving $\frac{1}{2}$ inside the logarithm.

$\log_{3} (4 y) + \log_{3} (49^{\frac{1}{2}})$

Step 2.2

Rewrite $49$ as $7^{2}$ .

$\log_{3} (4 y) + \log_{3} ({(7^{2})}^{\frac{1}{2}})$

Step 2.3

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log_{3} (4 y) + \log_{3} (7^{2 (\frac{1}{2})})$

Step 2.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.4.1

Cancel the common factor.

$\log_{3} (4 y) + \log_{3} (7^{2 (\frac{1}{2})})$

Step 2.4.2

Rewrite the expression.

$\log_{3} (4 y) + \log_{3} (7^{1})$

Step 2.5

Evaluate the exponent.

$\log_{3} (4 y) + \log_{3} (7)$

Step 3

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{3} (4 y \cdot 7)$

Step 4

Multiply $7$ by $4$ .

$\log_{3} (28 y)$