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Home Q & A Board Science-Related Homework Help Mathematics
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onesweetlady02 onesweetlady02
wrote...
11 years ago
7(4^x) = 3(5^x)

Do i "let y=4^x" or something?
It's my homework and i am completely stuck.
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wrote...
#1
11 years ago
first I'd divide by 7 (or 3) to get the factors on one side:
4^x = 3/7 5^x
Then you take the log (any kind of log works, natural log ln is usually preferred)
ln(4^x) = ln(3/7*5^x)
A factor in the log can be written as ln(3/7) + ln(5^x)
now the exponent of something in a log can be written as a factor of the log:
x*ln(4) = ln(5/7) + x*ln(5)
now you can subtract x*ln(5):
x*(ln 4 - ln 5) = ln(5/7)
ln 4 - ln 5 = ln(4/5)
so x = ln(3/7)/ln(4/5)
all that stuff on the right side is just numbers, you can plug that into a calculator.
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