SOLUTION: Log (3x-1) base 5 all over 1 + log x base 5 = 3+log 2 base 10

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Log (3x-1) base 5 all over 1 + log x base 5 = 3+log 2 base 10      Log On


   

Question 1204499: Log (3x-1) base 5 all over 1 + log x base 5 = 3+log 2 base 10
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
log+%285%2C%283x-1%29%29%2F%28+1+%2B+log%285%2C+x%29%29=+3%2Blog%2810%2C+2%29.....write 1 as log%285%2C5%29 and 3 as log%2810%2C10%5E3%29

.....log%285%2C5%29%2B+log%285%2C+x%29=log%285%2C5x%29 and log%2810%2C10%5E3%29%2Blog%2810%2C+2%29=log%282%2A10%5E3%29


log+%285%2C%283x-1%29%29%2F+log%285%2C+5x%29=++log%2810%2C2%2A10%5E3%29....change left side to base 10

%28log+%283x-1%29%2Flog%285%29%29%2F+%28log%285x%29%2Flog%285%29%29=++log%2810%2C2000%29...simplify



log+%283x-1%29%2F+log%285x%29=++log%2810%2C2000%29

log+%285x%2C3x-1%29=+log%2810%2C2000%29

using calculator, we get numerical solutions:
x ≈ 0.128612+%2B+0.12788%2Ai
x ≈ 0.128612+-+0.127883%2Ai