# Step-by-step Solution

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## Step-by-step solution

Problem to solve:

$2log\left(x\right)-log\left(x+6\right)=0$

Learn how to solve logarithmic equations problems step by step online.

$\log \left(x^2\right)-\log \left(x+6\right)=0$

Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation 2log(10,x)-log(10,x+6)=0. Apply the formula: a\log_{b}\left(x\right)=\log_{b}\left(x^a\right), where a=2 and b=10. The difference of two logarithms of equal base b is equal to the logarithm of the quotient: \log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right). Rewrite the number 0 as a logarithm of base 10. 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.

$x=3$
$2log\left(x\right)-log\left(x+6\right)=0$

### Main topic:

Logarithmic Equations

~ 0.08 s