Final Answer
$x=2\sqrt{5},\:x=-2\sqrt{5}$
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Step-by-step Solution
Specify the solving method
1
Express the numbers in the equation as logarithms of base $5$
$\log_{5}\left(x^2+5\right)=\log_{5}\left(5^{2}\right)$
Learn how to solve logarithmic equations problems step by step online.
$\log_{5}\left(x^2+5\right)=\log_{5}\left(5^{2}\right)$
Learn how to solve logarithmic equations problems step by step online. Solve the logarithmic equation log5(x^2+5)=2. Express the numbers in the equation as logarithms of base 5. Calculate the power 5^{2}. 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. We need to isolate the dependent variable , we can do that by simultaneously subtracting 5 from both sides of the equation.
Final Answer
$x=2\sqrt{5},\:x=-2\sqrt{5}$