simple math question?

Question

if i have an expression 5^x = 15625. how do i solve for x? how would i do this on a scientific calculator?

Answer 1

x = log, base 5, of 15625

log(base a) of b = log b/log a

x=log15625/log 5

press buttons: 15625 (log) divide 5 (log)

Answer 2

1. Enter 5 into your calculator.
2. Multiply by 5
3. Look at the answer if it matches what you are looking for you are done. Other wise go back to step 1.

so,
5 * 5 = 25 or 5^2
25 * 5 = 125 or 5^3
125 * 5 = 625 or 5^4
625 * 5 = 3125 or 5^5
3125 * 5 = 15625 or 5^6

This is just in case you dont have a scientific calculator, or if you want to verify your answer. Note most calculators have a feature that will do the last operation over agan if you press = again. So doing 5*5 = gets you 5^2, then count up from there for every time you need to hit = before you get the number you are looking for.

I was stuck in that age between the abacus and the scientific calculator.

Answer 3

You need to convert this to x = log (base 5) 15625. Use the log function on your calc

since log(base 5) of 15625 = log (base 10) of 15625/log(base 10) of 5, you can use your calc to do, log 15625/log 5.

The answer is 6, since 5^6 = 15625

Answer 4

You need to take the 1/5 root of both sides of the equation. 1/5 is equal to 0.2. So x = 15625 ^ 0.2

Answer 5

use natural logs (ln)

Someone else can detail more fully how to use logs and natural logs, but...

ln(5) [times] x = ln(15625)
now it becomes an algebra problem
1.6094 [times] x = 9.6566
x = 9.6566/1.6094
x = 6

Answer 6

5^x=15625 =>
ln(5^x)= ln(15625) =>
ln(5)^x = ln(15625) =>
x*ln(5)=ln(15625)=>
x={ln(15625) / ln(5) }

so you can calculate it!
isn't it easy?

Answer 7

1/5 = 0.2 on Fraction Percantage i guess.
And your answer will be I5625^0.2