Rewrite the following expression by using the laws of logarithms.

Question

ln(e^xR⁶)

 

A. xe+6ln(R)

B. e+R⁶

C. x+6ln(R)

D. x+ln(6R)

E. 1+6ln(R)

F. None of the above.

Answer 1

According to the rules of logarithms, the arguments of a single log can be broken down to a summation of logs.

 

Multiplying arguments yields the summation of logs.

Dividing arguments yields he difference of logs.

Raising a power to a log's base argument yields that the exponent is the coefficient of the log.

 

Therefore,

 

ln(e^xR⁶) =

 

ln(e^x) + ln(R⁶) =

 

xln(e) + 6ln(R)

 

 

Using the fact that  ln(e)=1,

 

x + 6ln(R)

 

 

This matches choice C.