What is 1/2 (log_{5}(x^6)+log_{5}(x^3)) ?

The solution to 1/2 (log_{5}(x^6)+log_{5}(x^3)) is (9log_{5}(x))/2

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simplify 1/2 (log_{5}(x^6)+log_{5}(x^3))

simplify

\frac{1}{2} (lo g_{5} (x^{6}) + lo g_{5} (x^{3}))

\frac{9 lo g _{5} ( x )}{2}

Solution steps

\frac{1}{2} (lo g_{5} (x^{6}) + lo g_{5} (x^{3}))

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{5} (x^{6}) = 6 lo g_{5} (x)

= \frac{1}{2} (6 lo g_{5} (x) + lo g_{5} (x^{3}))

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{5} (x^{3}) = 3 lo g_{5} (x)

= \frac{1}{2} (6 lo g_{5} (x) + 3 lo g_{5} (x))

Add similar elements:

6 lo g_{5} (x) + 3 lo g_{5} (x) = 9 lo g_{5} (x)

= \frac{1}{2} \cdot 9 lo g_{5} (x)

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 9 lo g _{5} ( x )}{2}

Multiply the numbers:

1 \cdot 9 = 9

= \frac{9 lo g _{5} ( x )}{2}

lo g_{a} (\frac{x ^{7}}{y z ^{8}})

lo g_{7} ((5) (c))

lo g_{10} (3 x)

lo g_{5} (2 x) + lo g_{5} (x - 1)

What is 1/2 (log_{5}(x^6)+log_{5}(x^3)) ?
The solution to 1/2 (log_{5}(x^6)+log_{5}(x^3)) is (9log_{5}(x))/2