What is the answer to log_{x}(3)=3log_{3}(9)x ?

The answer to log_{x}(3)=3log_{3}(9)x is x=(ln(3)}{6\W_{0}(\frac{ln(3))/6)}

Solve for x: log_{x}(3)=3log_{3}(9)x

The solution is x=(ln(3)}{6\W_{0}(\frac{ln(3))/6)}

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lo g_{x} (3) = 3 lo g_{3} (9) x

x = \frac{ln ( 3 )}{6 W _{0} ( \frac{l n ( 3 )}{6} )}

Decimal Notation

x = 1.16948 \dots

Solution steps

lo g_{x} (3) = 3 lo g_{3} (9) x

f (x) = g (x),

then

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

x^{l o g_{x} (3)} = x^{3 l o g_{3} (9) x}

Simplify

x^{l o g_{x} (3)} : 3

Simplify

x^{3 l o g_{3} (9) x} : x^{6 x}

3 = x^{6 x}

Solve

3 = x^{6 x} : x = \frac{ln ( 3 )}{6 W _{0} ( \frac{l n ( 3 )}{6} )}

x = \frac{ln ( 3 )}{6 W _{0} ( \frac{l n ( 3 )}{6} )}

Verify Solutions:

x = \frac{ln ( 3 )}{6 W _{0} ( \frac{l n ( 3 )}{6} )}

True

The solution is

x = \frac{ln ( 3 )}{6 W _{0} ( \frac{l n ( 3 )}{6} )}

lo g_{10} (3^{3 x + 1}) = 9^{x}

lo g_{3} (4 x + 6) = 4

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

ln (x - 3) = ln (7 x - 23) - ln (x + 1)

- x + 4 = ln (x)

What is the answer to log_{x}(3)=3log_{3}(9)x ?
The answer to log_{x}(3)=3log_{3}(9)x is x=(ln(3)}{6\W_{0}(\frac{ln(3))/6)}
Solve for x: log_{x}(3)=3log_{3}(9)x
The solution is x=(ln(3)}{6\W_{0}(\frac{ln(3))/6)}