What is log_{9}(9x^4)+log_{sqrt(3)}(sqrt(x)) ?

The solution to log_{9}(9x^4)+log_{sqrt(3)}(sqrt(x)) is 1+4log_{9}(x)+2log_{3}(sqrt(x))

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simplify log_{9}(9x^4)+log_{sqrt(3)}(sqrt(x))

simplify

lo g_{9} (9 x^{4}) + lo g_{3} (x)

1 + 4 lo g_{9} (x) + 2 lo g_{3} (x)

Solution steps

lo g_{9} (9 x^{4}) + lo g_{3} (x)

Simplify

lo g_{9} (9 x^{4}) : 1 + 4 lo g_{9} (x)

= (1 + 4 lo g_{9} (x)) + lo g_{3} (x)

Apply rule:

(a) = a

(1 + 4 lo g_{9} (x)) = 1 + 4 lo g_{9} (x)

= 1 + 4 lo g_{9} (x) + lo g_{3} (x)

Simplify

lo g_{3} (x) : 2 lo g_{3} (x)

= 1 + 4 lo g_{9} (x) + 2 lo g_{3} (x)

2 lo g_{10} (8) - 3 lo g_{10} (x)

- \frac{ln ( 3 ) - ln ( 2 )}{ln ( 2 )}

\frac{1}{2} lo g_{10} (x) - 6 lo g_{10} (y)

lo g_{2} ((m + n) \cdot p)

lo g_{10} (\frac{x}{1000 y ^{8}})

What is log_{9}(9x^4)+log_{sqrt(3)}(sqrt(x)) ?
The solution to log_{9}(9x^4)+log_{sqrt(3)}(sqrt(x)) is 1+4log_{9}(x)+2log_{3}(sqrt(x))