how would i solve for x? 15= 47.898 * .962445^x?

Question

explain all steps please..im an idiot

Answer 1

15= 47.898 * .962445^x
15/47.898 = .962445^x
.313 = .962445^x
log .313 = log .962445^x
log .313 = xlog .962445
log .313/log .962445 = x
30.361= x

Answer 2

Don't pay attention to the second asnwer. The first answer is correct.
Also, just in case you've never gone over natural logs, the answer could also have been obtained by following those steps but using the common log, base 10.

Answer 3

15 = 47.898 *.962445^x
15/47.898 = .962445^x .... reduces it to just the power function

let 15/47.898 be represented as N

x = (log N)/(log .962445) changes the base of the logarithim to the .962445, and giving you the value of x simultaneously

Answer 4

15= 47.898 * .962445^x divide both sides by 47.898
15/47.898=0.962445^x take ln of both sides
ln(15/47.898)=x ln 0.962445 divide both sides by ln 0.962445
x=ln (15/47.898) / ln (0.962445)
x=30.33107