Exercise
$2\log\left(x-1\right)=\log\left(5\right)$
Step-by-step Solution
Learn how to solve properties of logarithms problems step by step online. Solve the logarithmic equation 2log(x+-1)=log(5). Apply the formula: a\log_{b}\left(x\right)=\log_{b}\left(x^a\right), where a=2, b=10 and x=x-1. For two logarithms of the same base to be equal, their arguments must be equal. In other words, if \log(a)=\log(b) then a must equal b. Removing the variable's exponent. Cancel exponents 2 and 1.
Solve the logarithmic equation 2log(x+-1)=log(5)
Final answer to the exercise
$x=1+\sqrt{5},\:x=1-\sqrt{5}$