SOLUTION: using the law of logarithms, solve for the following indicial equation for x each correct to three decimal places 4 to the power of 2x-1 = 5 to the power of x+2 4^2x-1 = 5^x+

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: using the law of logarithms, solve for the following indicial equation for x each correct to three decimal places 4 to the power of 2x-1 = 5 to the power of x+2 4^2x-1 = 5^x+      Log On


   

Question 763448: using the law of logarithms, solve for the following indicial equation for x each correct to three decimal places
4 to the power of 2x-1 = 5 to the power of x+2
4^2x-1 = 5^x+2
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
(1) 4%5E%282x-1%29+=+5%5E%28x%2B2%29
Take the LOG of each side to get
(2) %282x-1%29%2ALOG%284%29+=+%28x%2B2%29%2ALOG%285%29 or
(3) 2%2ALOG%284%29%2Ax+-+LOG%284%29+=+LOG%285%29%2Ax+%2B+2%2ALOG%285%29 or
(4) 2%2ALOG%284%29%2Ax+-+LOG%285%29%2Ax+=+LOG%284%29+%2B+2%2ALOG%285%29 or
(5) %28LOG%284%5E2%29-LOG%285%29%29%2Ax+=+LOG%284%29%2BLOG%285%5E2%29 or
(6) %28LOG%2816%29-LOG%285%29%29%2Ax+=+LOG%284%29%2BLOG%2825%29 or
(7) LOG%2816%2F5%29%2Ax+=+LOG%284%2A25%29 or
(8) LOG%283.2%29%2Ax+=+LOG%28100%29 or
(9) x+=+LOG%28100%29%2FLOG%283.2%29 or
(10)x+=+2%2F0.50515... or
(11) x+=+3.959
To check put x of (11) into (1) and you will get
(12) 14638 = 14638
Answer: x = 3.959