SOLUTION: Determine the value of ab if https://imgur.com/a/1u4d55h

Question 1153085: Determine the value of ab if https://imgur.com/a/1u4d55h
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

log(8,a)+log(4,b^2)=5
log(8,b)+log(4,a^2)=7

.....eq.1
.....eq.2
----------------------------------

.....eq.1, solve for
......change to base

....simplify,

...simplify

............eq.1a

go to
.....eq.2, do same as above

.........eq.2a

from eq.1a and eq.2a we have

....simplify

=>
go to
............eq.1a, substitute

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Change the bases of each logarithm, knowing that and .

Simplify using the exponent rule of logarithms.

Change the two equations to exponential form. (See below for an alternative method for solving the problem from this point.)

Multiply the two equations together:

ANSWER: ab = 512

It's more work; but you could also solve the problem by using elimination to solve the pair of equations in the two unknowns, and .

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