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

The answer to log_{x}(3)=log_{3}(9)x^3 is x=\sqrt[3]{(ln(3)*3}{2\W_{0}(\frac{3ln(3))/2)}}

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

The solution is x=\sqrt[3]{(ln(3)*3}{2\W_{0}(\frac{3ln(3))/2)}}

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

x = 3 \frac{ln ( 3 ) \cdot 3}{2 W _{0} ( \frac{3 l n ( 3 )}{2} )}

Decimal

x = 1.29090 \dots

Solution steps

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

f (x) = g (x),

then

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

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

Simplify

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

Simplify

x^{l o g_{3} (9) x^{3}} : x^{2 x^{3}}

3 = x^{2 x^{3}}

Solve

3 = x^{2 x^{3}} : x = 3 \frac{ln ( 3 ) \cdot 3}{2 W _{0} ( \frac{3 l n ( 3 )}{2} )}

x = 3 \frac{ln ( 3 ) \cdot 3}{2 W _{0} ( \frac{3 l n ( 3 )}{2} )}

Verify Solutions:

x = 3 \frac{ln ( 3 ) \cdot 3}{2 W _{0} ( \frac{3 l n ( 3 )}{2} )}

True

The solution is

x = 3 \frac{ln ( 3 ) \cdot 3}{2 W _{0} ( \frac{3 l n ( 3 )}{2} )}

lo g_{10} (x^{2} + 4 x - 2) = 1

lo g_{4} (x) + 4 lo g_{x} (4) = 5

lo g_{4} (x^{2} + 5 x - 8) = 2

lo g_{x} (24) = 5

0.56 = ln (y)

What is the answer to log_{x}(3)=log_{3}(9)x^3 ?
The answer to log_{x}(3)=log_{3}(9)x^3 is x=\sqrt[3]{(ln(3)*3}{2\W_{0}(\frac{3ln(3))/2)}}
Solve for x: log_{x}(3)=log_{3}(9)x^3
The solution is x=\sqrt[3]{(ln(3)*3}{2\W_{0}(\frac{3ln(3))/2)}}