Question 130682
{{{2log(7,(x))=2+log(7,(16))}}} Start with the given equation. 



{{{log(7,(x^2))=2+log(7,(16))}}} Rewrite the left side using the identity  {{{log(b,(x^y))=y*log(b,(x))}}}



{{{log(7,(x^2))-log(7,(16))=2}}} Subtract {{{log(7,(16))}}} from both sides



{{{log(7,(x^2/16))=2}}} Combine the logs using the identity {{{log(b,(A))-log(b,(B))=log(b,(A/B))}}}




{{{7^2=x^2/16}}} Rewrite the equation using the property: {{{log(b,(x))=y}}} ====> {{{b^y=x}}}



{{{49=x^2/16}}} Evaluate {{{7^2}}} to get 49



{{{784=x^2}}} Multiply both sides by 16



{{{sqrt(784)=x}}} Take the square root of both sides



{{{28=x}}} Take the square root of 784 to get 28




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Answer:


So the solution is {{{x=28}}}