SOLUTION: 5^(2x+1)÷25=125

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Question 1076450: 5^(2x+1)÷25=125
Found 2 solutions by addingup, MathTherapy:
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
5^(2x+1)÷25=125
multiply both sides times 25
5^(2x+1) = 3125
log(5^(2x+1)) = log(3125)
Remember the rules of logs? The log of a number raised to a power is the power times the log of the number, like this:
(2x+1)log(5) = log(3125)
2x+1 = (log(3125))/log(5)
2x+1 = log_5(3125)
2x = (log_5(3125))-1
2x = 5-1
2x = 4
x = 2

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
5^(2x+1)÷25=125
matrix%281%2C3%2C+5%5E%282x+%2B+1%29%2F25%2C+%22=%22%2C+125%29

matrix%281%2C3%2C+5%5E%282x+%2B+1%29%2F5%5E2%2C+%22=%22%2C+5%5E3%29

matrix%281%2C3%2C+5%5E%282x+%2B+1%29%2C+%22=%22%2C+5%5E3+%2A+5%5E2%29 ------- Cross-multiplying

matrix%281%2C3%2C+5%5E%282x+%2B+1%29%2C+%22=%22%2C+5%5E%283+%2B+2%29%29 ------ Applying a%5Eb+%2A+a%5Ec+=+a%5E%28b+%2B+c%29

2x + 1 = 3 + 2 ---------- Bases are equal and so are the exponents

2x = 4

highlight_green%28matrix%281%2C5%2C+x%2C+%22=%22%2C+4%2F2%2C+or%2C+2%29%29