The solution of the equation log7 log5 ( √ x + 5 + √ x) = 0 is ....

Question

The solution of the equation log7 log5 ( √ x + 5 + √ x) = 0 is .... (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Given equation is log7 log5 ( √ x + 5 + √ x) = 0 ⇒ log5 ( √ x + 5 + √ x) = 1 ⇒ √ x + 5 + √ x = 5 ⇒ √ x + 5 = 5 - √ x ⇒ x + 5 = 25 + x - 10 √ x ⇒ 10 √ x = 20 ⇒ √ x = 2 ⇒ x = 4

Q. The solution of the equation
$l o g_{7} l o g_{5} (x + 5 + x) = 0$ is ....

Given equation is
$l o g_{7} l o g_{5} (x + 5 + x) = 0$
$\Rightarrow l o g_{5} (x + 5 + x) = 1$
$\Rightarrow x + 5 + x = 5$
$\Rightarrow x + 5 = 5 - x$
$\Rightarrow x + 5 = 25 + x - 10 x$
$\Rightarrow 10 x = 20$
$\Rightarrow x = 2$
$\Rightarrow x = 4$

Q. The solution of the equation log7​log5​(x+5​+x​)=0 is ....

Given equation is log7​log5​(x+5​+x​)=0 ⇒log5​(x​+5+x​)=1 ⇒x+5​+x​=5 ⇒x+5​=5−x​ ⇒x+5=25+x−10x​ ⇒10x​=20 ⇒x​=2 ⇒x=4

Q. The solution of the equation
$l o g_{7} l o g_{5} (x + 5 + x) = 0$ is ....

Given equation is
$l o g_{7} l o g_{5} (x + 5 + x) = 0$
$\Rightarrow l o g_{5} (x + 5 + x) = 1$
$\Rightarrow x + 5 + x = 5$
$\Rightarrow x + 5 = 5 - x$
$\Rightarrow x + 5 = 25 + x - 10 x$
$\Rightarrow 10 x = 20$
$\Rightarrow x = 2$
$\Rightarrow x = 4$