SOLUTION: Given that log base2 to 3 = x and log base2 to 5 = y, write log base2 to 8/135 in terms of x and y

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Question 1177562: Given that log base2 to 3 = x and log base2 to 5 = y, write log base2 to 8/135 in terms of x and y
Found 2 solutions by greenestamps, MathLover1:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


"log base 2 OF 3", not "log base 2 to 3"....

log%282%2C%288%2F135%29%29%29
= log%282%2C%28%282%5E3%29%2F%28%283%5E3%29%285%29%29%29%29
= 3log%282%2C2%29-%283log%282%2C3%29%2Blog%282%2C5%29%29
= 3%281%29-%283x%2By%29
= 3-3x-y

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Given:
log%282%2C+3%29+=+x
log%282%2C+5%29+=+y

write log%282%2C8%2F135%29 in terms of x and y

log%282%2C8%2F135%29
log%282%2C2%5E3%2F%283%5E3%2A5%29+%29
log%282%2C2%5E3%29-log%282%2C3%5E3%2A5+%29
3log%282%2C2%29-%28log%282%2C3%5E3%29%2Blog%282%2C5+%29%29
3log%282%2C2%29-%283log%282%2C3%29%2Blog%282%2C5+%29%29
3log%282%2C2%29-3log%282%2C3%29-log%282%2C5+%29............substitute log%282%2C3%29 and log%282%2C5%29
3log%282%2C2%29-3x-y