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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Decimal Notation

x = - 0.19967 \dots

Solution steps

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

f (x) = g (x),

then

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

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

Simplify

1 0^{l o g_{10} (x^{2})} : x^{2}

x^{2} = 1 0^{2 x - 1}

Solve

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

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

Verify Solutions:

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

True

The solution is

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

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

lo g_{10} (x) (100) = 2

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

lo g_{5} (t) = 3

lo g_{10} (x) = 0.8537

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