Question
Log243-log64-log3 with the base 3,2,root3 give me a simplify of these
Answers
Reiny
I read that as
log<sub>3</sub> 243 - log<sub>2</sub> 64 - log<sub>√3</sub> 3
notice that 3^5 = 243 , 2^6 = 64 and (√3)^2 = 3
then:
log<sub>3</sub> 243 - log<sub>2</sub> 64 - log<sub>√3</sub> 3
= 5 - 6 - 2
= -3
log<sub>3</sub> 243 - log<sub>2</sub> 64 - log<sub>√3</sub> 3
notice that 3^5 = 243 , 2^6 = 64 and (√3)^2 = 3
then:
log<sub>3</sub> 243 - log<sub>2</sub> 64 - log<sub>√3</sub> 3
= 5 - 6 - 2
= -3
Anonymous
log 3 9 +log 243 9+2log 3 9
Praket Tiwaskar
Question: log3 243 - log2 64 + log√3 3
This can also be written as:
log3 3^5 - log2 2^6 + log√3 √3^2
= 5log3 3 - 6log2 2 + 2log√3 √3 [Since loge m^n = nloge m]
= 5(1) - 6(1) + 2(1) [Since logm m = 1]
= 5-6+2
= 1
This can also be written as:
log3 3^5 - log2 2^6 + log√3 √3^2
= 5log3 3 - 6log2 2 + 2log√3 √3 [Since loge m^n = nloge m]
= 5(1) - 6(1) + 2(1) [Since logm m = 1]
= 5-6+2
= 1