SOLUTION: use log_(5)2=0.4307 and log_(5)3= 0.6826 to approximate the value of log_(5)54 thank you

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: use log_(5)2=0.4307 and log_(5)3= 0.6826 to approximate the value of log_(5)54 thank you      Log On


   

Question 1074819: use log_(5)2=0.4307 and log_(5)3= 0.6826 to approximate the value of log_(5)54
thank you
Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The log5 (6)=log 5 (2*3)=log 5(2)+log 5 (3)
That is 1.1133
log 5 (54)=log 5 (9*6)=log 5(9)+log 5(6)
But log 5(9)=log 5(3^2)=2 log 5(3)=1.3652
log 5 (6)=1.1133
The approximate answer is 1.3652+1.1133=2.4785 ANSWER
5^2.4785=54.00

Answer by MathTherapy(10806) About Me  (Show Source):
You can put this solution on YOUR website!
use log_(5)2=0.4307 and log_(5)3= 0.6826 to approximate the value of log_(5)54
thank you
log+%285%2C+2%29+=+0.4307		log+%285%2C+3%29+=+0.6826

log+%285%2C+54%29+=+0.4307 ======> log+%285%2C+%282+%2A+27%29%29 ======> log+%285%2C+%282+%2A+3%5E3%29%29 ======> log+%285%2C+2%29+%2B+log+%285%2C+3%5E3%29
log+%285%2C+2%29+%2B+3+%2A+log+%285%2C+3%29 	
0.4307 + 3(0.6826) -------- Substituting 0.4307 for log+%285%2C+2%29, and 0.6826 for log+%285%2C+3%29
highlight_green%28matrix%281%2C3%2C+log+%285%2C+54%29%2C+%22=%22%2C+2.4785%29%29