Equation - Exponential Function

Mar 2010
21
0
Hello guys.

I know this must be pretty basic. But, I don't get it.

How do I solve 0,6 = 0,95^x ?

This is from an equation. I got up to this point, but I can't finish it. Any help would be appreciated.
 

earboth

MHF Hall of Honor
Jan 2006
5,854
2,553
Germany
Hello guys.

I know this must be pretty basic. But, I don't get it.

How do I solve 0,6 = 0,95^x ?

This is from an equation. I got up to this point, but I can't finish it. Any help would be appreciated.
1. Use logarithms:

\(\displaystyle 0,6 = 0,95^x~\implies~x=\log_{0.95}(0.6)\)

2. Now use the base-change-formula:

\(\displaystyle x=\log_{0.95}(0.6)~\implies~x=\frac{\ln(0.6)}{\ln(0.95)}\)

3. Hint: Better use a decimal point to separate the integer part from the fraction part of a number.
 
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e^(i*pi)

MHF Hall of Honor
Feb 2009
3,053
1,333
West Midlands, England
Hello guys.

I know this must be pretty basic. But, I don't get it.

How do I solve 0,6 = 0,95^x ?

This is from an equation. I got up to this point, but I can't finish it. Any help would be appreciated.
\(\displaystyle \ln(0.6) = x\ln(0.95)\)

\(\displaystyle x = \frac{\ln(0.6)}{\ln(0.95)}\)
 
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Reactions: Alvy