Log and Ln Problem - Matching Equations

[pizbot]

Homework Statement

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

Homework 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

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

 

[jedishrfu]

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

 

[SammyS]

Homework Statement

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

Homework 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

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

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.

 

[Mark44]

Homework Equations

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

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

 

[Joffan]

What is your hardness value?