What is the answer to log_{5}(x^3)+13x-5=0 ?

The answer to log_{5}(x^3)+13x-5=0 is x=(3\W_{0}((13ln(5)e^{\frac{5ln(5))/3})/(3))}{13ln(5)}

Solve for x: log_{5}(x^3)+13x-5=0

The solution is x=(3\W_{0}((13ln(5)e^{\frac{5ln(5))/3})/(3))}{13ln(5)}

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lo g_{5} (x^{3}) + 13 x - 5 = 0

x = \frac{3 W _{0} ( \frac{13 l n ( 5 ) e ^{\frac{5 l n ( 5 )}{3}}}{3} )}{13 ln ( 5 )}

Decimal Notation

x = 0.48760 \dots

Solution steps

lo g_{5} (x^{3}) + 13 x - 5 = 0

Move

13 x

to the right side

lo g_{5} (x^{3}) - 5 = - 13 x

Move

5

to the right side

lo g_{5} (x^{3}) = - 13 x + 5

Apply log rules

lo g_{5} (x) = \frac{- 13 x + 5}{3}

f (x) = g (x),

then

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

5^{l o g_{5} (x)} = 5^{\frac{- 13 x + 5}{3}}

Simplify

5^{l o g_{5} (x)} : x

x = 5^{\frac{- 13 x + 5}{3}}

Solve

x = 5^{\frac{- 13 x + 5}{3}} : x = \frac{3 W _{0} ( \frac{13 l n ( 5 ) e ^{\frac{5 l n ( 5 )}{3}}}{3} )}{13 ln ( 5 )}

x = \frac{3 W _{0} ( \frac{13 l n ( 5 ) e ^{\frac{5 l n ( 5 )}{3}}}{3} )}{13 ln ( 5 )}

Verify Solutions:

x = \frac{3 W _{0} ( \frac{13 l n ( 5 ) e ^{\frac{5 l n ( 5 )}{3}}}{3} )}{13 ln ( 5 )}

True

The solution is

x = \frac{3 W _{0} ( \frac{13 l n ( 5 ) e ^{\frac{5 l n ( 5 )}{3}}}{3} )}{13 ln ( 5 )}

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

lo g_{x} (x^{2}) = lo g_{8} (16 x)

lo g_{10} (x) = 18

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

lo g_{10} (x) + x = 0

What is the answer to log_{5}(x^3)+13x-5=0 ?
The answer to log_{5}(x^3)+13x-5=0 is x=(3\W_{0}((13ln(5)e^{\frac{5ln(5))/3})/(3))}{13ln(5)}
Solve for x: log_{5}(x^3)+13x-5=0
The solution is x=(3\W_{0}((13ln(5)e^{\frac{5ln(5))/3})/(3))}{13ln(5)}