Solve the equation for x. \(\displaystyle{\ln{{\left({\ln{{3}}}{x}\right)}}}={0}\)

Guadalupe Glass

Guadalupe Glass

Answered question

2022-03-22

Solve the equation for x. ln(ln3x)=0

Answer & Explanation

allemelrypi0e

allemelrypi0e

Beginner2022-03-23Added 11 answers

Logarithm is inverse of exponentiations. A logarithm is easy method to express large number and to perform arithmetic operation on them. Multiplication and division can be written in form of addition and subtraction while operating logarithms
There are various rules involved in performing logarithmic operations, some required for question are as follows
Product rule logamn=logam+logan
Exponent rule logam=nn=an
The given expression is ln(ln3x)=0, use exponent rule to solve the equation for x
ln(ln3x)=0
ln3x=e0  (using exponent rule)  
ln3x=1
3x=e1  (using exponent rule)  
x=e3
Therefore, value of x is e3 which is equal to 0.906.

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