# Logarithms and scientific calculator

1. Nov 2, 2014

### ilii

1. The problem statement, all variables and given/known data
y= -2log3(x-3) -1

2. Relevant equations
I am using a SHARP EL-546W scientific calculator, and I do not know what steps to take in order to find a point given an x value. i.e. if x=3, then y=6. I cannot seem to get 6 on my own and I have tried a wide variety of methods and button sequences.

3. The attempt at a solution
Please instruct me on how to find logs on my calculator, thank you

2. Nov 2, 2014

### Ray Vickson

I cannot figure out what is your expression. Do you mean $y = -2 \log_{3}(x-3) -1$ or $y = -2 (\log 3)(x-3) -1$ or $y = -2 \log(3(x-3)) - 1$. If you mean one of the last two what "base" are you using for the logarithm? Base 10? Base $e$? You must use parentheses when typing formulas, tp make your meaning clear.

Anyway, you will NEVER get y = 6 when you put x = 3. If you mean either the first or third form above, the logarithm does not exist when x = 3 because it would be log(0)---and there is no such thing---while if you mean the second one you would get y = -1 when x = 3.

3. Nov 2, 2014

### ilii

sorry, it is the first expression you mentioned

4. Nov 2, 2014

### Staff: Mentor

If x = 3, then x - 3 = 0, so log3(x - 3) is undefined.

5. Nov 2, 2014

### Ray Vickson

So, you want log to base 3. I am not familiar with your calculator, but most calculators do not have buttons for logs to arbitrary bases, but almost always allow you to choose between base 10 and base $e$. You can get $\log_3 w$ either in terms of $\log_{10} w$ or $\log_{e} w \equiv \ln w$. In fact, if you have two bases $a$ and $b$, you can get $\log_{a} w$ in terms of $\log_b w$:
$$\log_a w = \frac{\log_b w}{\log_b a},\\ \text{so }\\ \log_3 w = \frac{\log_{10} w}{\log_{10} 3}\\ \text{or}\\ \log_3 w = \frac{\ln w}{\ln 3}$$

6. Nov 2, 2014

### ilii

ok thank you for the help everything is clear now