What is the answer to G(x)=log_{9}(x^5) ?

The answer to G(x)=log_{9}(x^5) is x=-(5\W(-(2ln(3)G)/5))/(2ln(3)G)

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G(x)=log_{9}(x^5)

G (x) = lo g_{9} (x^{5})

x = - \frac{5 W ( - \frac{2 l n ( 3 ) G}{5} )}{2 ln ( 3 ) G}

Solution steps

G (x) = lo g_{9} (x^{5})

Apply log rules

lo g_{9} (x) = \frac{G x}{5}

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

9^{l o g_{9} (x)} = 9^{\frac{G x}{5}}

Simplify

9^{l o g_{9} (x)} : x

x = 9^{\frac{G x}{5}}

Solve

x = 9^{\frac{G x}{5}} : x = - \frac{5 W ( - \frac{2 l n ( 3 ) G}{5} )}{2 ln ( 3 ) G}

x = - \frac{5 W ( - \frac{2 l n ( 3 ) G}{5} )}{2 ln ( 3 ) G}

Verify Solutions:

x = - \frac{5 W ( - \frac{2 l n ( 3 ) G}{5} )}{2 ln ( 3 ) G}

True

The solution is

x = - \frac{5 W ( - \frac{2 l n ( 3 ) G}{5} )}{2 ln ( 3 ) G}

5 + ln (x + 2) = 8

2 lo g_{3} (x + 5) - lo g_{3} (9) = 2

(\frac{9}{5}) lo g_{4} (x) = - 2

lo g_{3} (x - 2) + lo g_{3} (x + 6) = 2

5 ln (4 x + 4) + 4 = - 11

What is the answer to G(x)=log_{9}(x^5) ?
The answer to G(x)=log_{9}(x^5) is x=-(5\W(-(2ln(3)G)/5))/(2ln(3)G)