Simplify/Condense 7* log base 5 of x+3* log base 5 of y^4

$7 \cdot \log_{5} (x) + 3 \cdot \log_{5} (y^{4})$

Step 1

Simplify each term.

Simplify $7 \log_{5} (x)$ by moving $7$ inside the logarithm.

$\log_{5} (x^{7}) + 3 \cdot \log_{5} (y^{4})$

Simplify $3 \log_{5} (y^{4})$ by moving $3$ inside the logarithm.

$\log_{5} (x^{7}) + \log_{5} ({(y^{4})}^{3})$

Multiply the exponents in ${(y^{4})}^{3}$ .

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

$\log_{5} (x^{7}) + \log_{5} (y^{4 \cdot 3})$

Multiply $4$ by $3$ .

$\log_{5} (x^{7}) + \log_{5} (y^{12})$

Step 2

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

$\log_{5} (x^{7} y^{12})$