What is 1/3 (3log_{7}(a)+2log_{7}(b)) ?

The solution to 1/3 (3log_{7}(a)+2log_{7}(b)) is log_{7}(a)+(2log_{7}(b))/3

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simplify 1/3 (3log_{7}(a)+2log_{7}(b))

simplify

\frac{1}{3} (3 lo g_{7} (a) + 2 lo g_{7} (b))

lo g_{7} (a) + \frac{2 lo g _{7} ( b )}{3}

Solution steps

\frac{1}{3} (3 lo g_{7} (a) + 2 lo g_{7} (b))

Apply the distributive law:

a (b + c) = ab + a c

\frac{1}{3} (3 lo g_{7} (a) + 2 lo g_{7} (b)) = \frac{1}{3} \cdot 3 lo g_{7} (a) + \frac{1}{3} \cdot 2 lo g_{7} (b)

= \frac{1}{3} \cdot 3 lo g_{7} (a) + \frac{1}{3} \cdot 2 lo g_{7} (b)

Simplify

\frac{1}{3} \cdot 3 lo g_{7} (a) + \frac{1}{3} \cdot 2 lo g_{7} (b) : lo g_{7} (a) + \frac{2 lo g _{7} ( b )}{3}

= lo g_{7} (a) + \frac{2 lo g _{7} ( b )}{3}

\frac{2}{3} ln (8) - 2 ln (4) + ln (24)

[\frac{1}{2} (ln ∣ x + 1 ∣ - ln ∣ x - 1 ∣)]

lo g_{2} (10) + lo g_{2} (20)

lo g_{c} (\frac{a ^{2} c}{b ^{3}})

2 lo g_{2} (x) - lo g_{2} (x + 3)

What is 1/3 (3log_{7}(a)+2log_{7}(b)) ?
The solution to 1/3 (3log_{7}(a)+2log_{7}(b)) is log_{7}(a)+(2log_{7}(b))/3