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How to sove an equation like 5^x=80?
That's the only thing my math teacher didn't get to for our finals review. I'm having trouble finding it in my math book. I'm pretty sure I know how to solve it but I want to make sure.
2 Answers
- Anonymous8 years agoFavorite Answer
Hi,
5^x = 80
log 5^x = log 80
x log 5 = log 80
. . . log 17
x = --------------
. . . log 80
I don't have a calculator on me so I can't give you the numeric value, But there's the process, hope it helps. You basically just apply log rules.
- MathBioMajorLv 78 years ago
80 = (5)(16), so we can rewrite the equation like this:
5^x = (5)(16)
5^x / 5 = (2)^4
5^(x - 1) = (2)^4.
Now we can take logs of both sides, and solve for x:
(x - 1) log 5 = 4 log 2
(x - 1) = (4 log 2 / log 5)
x = (4 log 2 / log 5) + 1.
x ~ 2.7227.
To verify the answer, raise 5 to that power:
5^(2.7227) ~ 80
79.99920 ~ 80.
The equation closely balances, so the answer is correct.