What is the answer to 3log_{10}(x-1)=3-2x ?

The answer to 3log_{10}(x-1)=3-2x is x=(3\W_{0}((2e^{\frac{ln(10))/3}ln(10))/(3))+2ln(10)}{2ln(10)}

Solve for x: 3log_{10}(x-1)=3-2x

The solution is x=(3\W_{0}((2e^{\frac{ln(10))/3}ln(10))/(3))+2ln(10)}{2ln(10)}

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3 lo g_{10} (x - 1) = 3 - 2 x

x = \frac{3 W _{0} ( \frac{2 e ^{\frac{l n ( 10 )}{3}} l n ( 10 )}{3} ) + 2 ln ( 10 )}{2 ln ( 10 )}

Decimal Notation

x = 1.71685 \dots

Solution steps

3 lo g_{10} (x - 1) = 3 - 2 x

Divide both sides by

3

lo g_{10} (x - 1) = \frac{3 - 2 x}{3}

f (x) = g (x),

then

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

1 0^{l o g_{10} (x - 1)} = 1 0^{\frac{3 - 2 x}{3}}

Simplify

1 0^{l o g_{10} (x - 1)} : x - 1

x - 1 = 1 0^{\frac{3 - 2 x}{3}}

Solve

x - 1 = 1 0^{\frac{3 - 2 x}{3}} : x = \frac{3 W _{0} ( \frac{2 e ^{\frac{l n ( 10 )}{3}} l n ( 10 )}{3} ) + 2 ln ( 10 )}{2 ln ( 10 )}

x = \frac{3 W _{0} ( \frac{2 e ^{\frac{l n ( 10 )}{3}} l n ( 10 )}{3} ) + 2 ln ( 10 )}{2 ln ( 10 )}

Verify Solutions:

x = \frac{3 W _{0} ( \frac{2 e ^{\frac{l n ( 10 )}{3}} l n ( 10 )}{3} ) + 2 ln ( 10 )}{2 ln ( 10 )}

True

The solution is

x = \frac{3 W _{0} ( \frac{2 e ^{\frac{l n ( 10 )}{3}} l n ( 10 )}{3} ) + 2 ln ( 10 )}{2 ln ( 10 )}

ln (5 x + 10) + ln (8) = 1

e^{2 l n (y)} = y + 12

- 3 + 2 ln (x) = 0

lo g_{4} (x) = 6 lo g_{x} (8)

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

What is the answer to 3log_{10}(x-1)=3-2x ?
The answer to 3log_{10}(x-1)=3-2x is x=(3\W_{0}((2e^{\frac{ln(10))/3}ln(10))/(3))+2ln(10)}{2ln(10)}
Solve for x: 3log_{10}(x-1)=3-2x
The solution is x=(3\W_{0}((2e^{\frac{ln(10))/3}ln(10))/(3))+2ln(10)}{2ln(10)}