2 Answers

Vinay S Shenoy · Answer 1 · 2021-02-10T19:55:25+0000

Answer:

Option B.

Explanation:

Let as consider the given equation:

$2\ln e^(\ln 2x)-\ln e^(\ln 10x)=\ln 30$

It can be written as

$2(\ln 2x)-(\ln 10x)=\ln 30$
$[\because \ln e^a=a]$

$\ln (2x)^2-(\ln 10x)=\ln 30$
$[\because \ln a^b=b\ln a]$

$\ln (4x^2)/(10x)=\ln 30$
$[\because \ln (a)/(b)=\ln a-\ln b]$

$\ln (2x)/(5)=\ln 30$

On comparing both sides, we get

(2x)/(5)=30

Multiply both sides by 5.

2x=150

Divide both sides by 2.

x=75

Therefore, the correct option is B.

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