Question

solve log base 7 log base 5 (√x+5)+√x) =0 ​

Answer 1

Given that :

$log_{7} log_{5}(\sqrt{x+5}+\sqrt{x} )=0$

Now taking $log_{7}$ on right side ,

Then the equation becomes ,

$log_{5}(\sqrt{x+5}+\sqrt{x} )=7^{0}$

Then,

$\sqrt{x+5}+\sqrt{x} =5^{1} =5\\\sqrt{x+5}=5-\sqrt{x}$

Now,

Taking square on both sides ,

we get,

$x+5=25+x-10\sqrt{x} x\\\sqrt{x} =2$

Hence, we get the value of x.

$x=4$