Equation - Exponential Function

**Alvy** · May 23rd 2010, 09:26 AM

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** · May 23rd 2010, 10:33 AM

Originally Posted by Alvy

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:

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

2. Now use the base-change-formula:

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

3. Hint: Better use a decimal point to separate the integer part from the fraction part of a number.

**e^(i*pi)** · May 23rd 2010, 10:33 AM

Originally Posted by Alvy

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.

$\ln(0.6) = x\ln(0.95)$

$x = \frac{\ln(0.6)}{\ln(0.95)}$

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