Question 385074: How do you solve 4^(8x)=7^(x+9) solve for x
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 4^(8x)=7^(x+9)
when x is in the exponent, use logarithms to solve
8x*log 4 = (x+9)* log 7
8x/(x+9) =log 7/log 4 =1.4037 (logarithm rule for working with exponents)
8x =(x+9) *1.4037=1.4037x+12.6333
8x-1.4037x =12.6333
6.5963x =12.6333
x =12.6333/6.5963 = 1.9152
check: 4^(8x)= 4^(8*1.9152) =167509909
7^(x+9) = 7^(1.9152+9) = 1676540798
the numbers do not check exactly because of rounding errors, but this is the method to use in solving these types of problems
|
|
|
