SOLUTION: Please help me find the expression equivalent for these two problems: 1. 5Logx - 1/4 Logb 2. If Log3=a and Log5=b,Find the expression for Log135 in terms of a and b.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help me find the expression equivalent for these two problems: 1. 5Logx - 1/4 Logb 2. If Log3=a and Log5=b,Find the expression for Log135 in terms of a and b.      Log On


   

Question 191025: Please help me find the expression equivalent for these two problems:
1. 5Logx - 1/4 Logb
2. If Log3=a and Log5=b,Find the expression for Log135 in terms of a and b.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


I'm presuming that x and b are the arguments of your log functions and that the base in each case is 10, so:



was what you intended.

First use:



to write:



Then use:



to write:



Then use:

The difference of the logs is the log of the quotient,



to write:



Then use:



to rationalize your denominator



hence:



Or convert back to fractional exponents if you wish:



==========================================

If and ,Find the expression for in terms of a and b.

so:



Use: The sum of the logs is the log of the product,



To write:



Use:



to write:



Then substitute a and b:




John