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Home Q & A Board Science-Related Homework Help Mathematics
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_biology _biology
wrote...
solved
11 years ago
Please can someone help me solve this equation, I believe the use of logarithms is required.

7^(x-3) = 4^(2x)

Thanks in advance, any help greatly appreciated.
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ilikepie1234 Author
wrote...
#1
11 years ago
4^m=7 where m is some unknown number.
(4^m)^(x-3)=4^(2x)
4^(mx-3m)=4^2x
mx-3m=2x
(m-2)x=3m
x=(3m)/(m-2)

now find m:
If 4^m=7 then log_base4 (7)=m
log_base4 (7) = log(7)/log(4) = m
Find m and plug it in to solve for x.
wrote...
#2
11 years ago
Definition of exponential functions to base a, where a is some constant says a^x = (e^(lna))^x= e^(lna)x so rewrite 7^(x-3) = e^(ln7)(x-3) and 4^(2x) = e^(ln4)(2x) so (ln7)(x-3) = (ln4)(2x) now move the variables to the same side and the numbers to the other so you have [(ln7)/(ln4)]=[(2x)/(x-3)] ln7 / ln4 = 1.403677461 = 2x/(x-3) simplify x=-7.061668992
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