Solve the logarithmic equation using properties of log

2 log x + log x =2 ?

Solve for x:
(3 log(x))/(log(10)) = 2

Divide both sides by 3/(log(10)):
log(x) = (2 log(10))/3

(2 log(10))/3  =  log(10^(2/3)):
log(x) = log(10^(2/3))

Cancel logarithms by taking exp of both sides:
Answer: |  x = 10^(2/3)

2 log x  + log x  =   2       [ note .....  2  can be written as log 100]

logx^2  + log x   = log 100

log [x^3]  = log 100       forget the logs

x^3  = 100       take the cube root of both sides

x =  ∛100  = 10^2/3

2 (log x) + log x =2

Omi67......you have made a slight error........

2log x    ≠  (log x)²

2log x   =  log x²   

 #2 Omi67

x=10^(2/3)=4.6415888336127788924100763509194

2 log x + log x =2 Substitute

2 log(4.6415888336127788924100763509194) + log(4.6415888336127788924100763509194)=2

[2 x 2/3] + 2/3 =2

1 1/3 + 2/3 =2

2 log x + log x = 2

3 log x = 2

log x = \(\frac{2}{3}\)

x = \(10^{\frac{2}{3}}\)=\(\sqrt[3]{100}\)

That's the same as CPhill's , and our guest's answer in #1