Answer:
[tex]x = 2\sqrt{10}[/tex]
Step-by-step explanation:
We have to solve for x from the logarithmic equation as follows:
[tex]\log x^{2} + \log 25 = 3[/tex]
⇒ [tex]\log 25x^{2} = 3[/tex]
{Since, using logarithmic property [tex]\log A + \log B = \log AB[/tex]}
Now, converting this logarithmic equation above into exponential equation we get,
[tex]25x^{2} = 10^{3}[/tex]
{Since we know that if [tex]\log_{10}a = b[/tex] then, we can write [tex]a = 10^{b}[/tex]}
⇒ [tex]25x^{2} = 1000[/tex]
⇒ [tex]x^{2} = 40[/tex]
⇒ [tex]x = 2\sqrt{10}[/tex] (Answer)
