SOLUTION: pls help me with this, log27 base x + log4 base y = 5 ; log27 base x - log4 base y = 1. find x and y

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Question 1134465: pls help me with this, log27 base x + log4 base y = 5 ; log27 base x - log4 base y = 1. find x and y
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
looks like you are solving two equations simultaneouosly with the twist that they involve logs.

the two equations are:

log27(x) + log4(y) = 5
log27(x) - log4(y) = 1

subtract the second equation from the first to get:

2 * log4(y) = 4

divide both sides of this equation by 2 to get log4(y) = 2

since log4(y) = 2, then both equations become:

log27(x) + 2 = 5
log27(x) - 2 = 1

add these two equations together to get:

2 * log27(x) = 6

divide this equaion by 2 to get log27(x) = 3.

your solution so far is:

log27(x) + log4(y) = 5 which becomes 3 + 2 = 5
log27(x) - log4(y) = 1 which becomes 3 - 2 = 1

the equations have been solved simultaneously and what is left is to find the value of x and y.

it was already determined that log27(x) = 3 and log4(y) = 2.

log27(x) = 3 if and only if 27^3 = x.
this makes x = 19683.

log4(y) = 2 if and only if 4^2 = y.
this makes y = 16.

your solution is that x = 19683 and y = 16.

you can confirm by using the base log conversion formula and your calculator.

log27(19683) = log(19683) / log(27) = 3

log4(16) = log(16) / log(4) = 2

solution is confirmed to be good.



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

pls help me with this, log27 base x + log4 base y = 5 ; log27 base x - log4 base y = 1. find x and y
The other person's answers are WRONG, so IGNORE them!

 





      













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