# Homework Help: Log and Ln Problem - Matching Equations

1. Jan 5, 2012

### pizbot

1. The problem statement, all variables and given/known data

I am trying to prove that the following equations are the same for a client, but keep getting different answers using a calculator.

2. Relevant equations

1- Cadmium concentration = e^0.86[In(hardness)]-3.2 μg/L

2 - Cadmium concentration = 10^0.86[log10(hardness)]-3.2 μg/L

3. The attempt at a solution

These are the answers I keep getting:

Cadmium concentration = e^0.86[In(hardness)]-3.2 μg/L = 0.649361 ug/L

Cadmium concentration = 10^0.86[log10(hardness)]-3.2 μg/L = 0.010051 ug/L

2. Jan 5, 2012

### Staff: Mentor

why would you think they are the same if you rewrite a little you'll see why:

cc = hardness * e^0.86 - 3.2

vs

cc = hardness * 10^0.86 - 3.2

to make them the same you need to fix the 0.86 power ie 10^y=e^0.86

3. Jan 5, 2012

### SammyS

Staff Emeritus
e ≈ 2.718281828459...

So, e ≠ 10 → e^0.86 ≠ 10^0.86, etc.

However, the display on many calculators does show E rather than 10 when displaying powers of ten, as in the following:

2.998✕108 will be shown as 2.998E8 .

Perhaps that's what you are thinking of.

4. Jan 5, 2012

### Staff: Mentor

There is no In function - it's ln (LN), short for logarithmus naturalis.

5. Jan 5, 2012