# Equation - Exponential Function

#### 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.

#### earboth

MHF Hall of Honor
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.

• Alvy

#### e^(i*pi)

MHF Hall of Honor
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.
$$\displaystyle \ln(0.6) = x\ln(0.95)$$

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

• Alvy