Find that values given that log a 25=0.846 and log a 4=0.173

Question

Find that values given that log a 25=0.846 and log a 4=0.173:

 

log a 10a

 

 

and

log a 0.25^25

Answer 1

log_a(10a) = log_a10 + log_aa = log_a(5·2) + 1

 

                                      = log_a (25^½4^½) + 1

 

                                      = ½(log_a25) + ½(log_a4) + 1

 

                                      =½(0.846) + ½(0.173) + 1

 

                                      = 1.5095

 

log_a(0.25)²⁵ = 25log_a(¼) = 25[log_a(1) - log_a4]

 

                                    = 25[0 - 0.173]

 

                                    = -4.325

Answer 2

first convert log_a10a to log_a10+log_aa = log_a10+1

do the same with log_a0.25²⁵=25log_a0.25

 

now you need to just deal with log_a10 and log_a0.25.  Can we do a combination of 25 and 4 (given logs) to get 10 and 0.25??

 

10 = sqrt(25*4) = (25*4)^1/2

0.25 = 1/4 = 4^-1 (negative exponents are reciprocals)

 

Replace the 10 and 0.25 with the above expressions and use your log rules to get them in terms of log_a25 and log_a4.  Then all you need to do is replace the given values and compute.

This should get you started.

Terri