Logarithms and scientific calculator

[ilii]

Homework Statement

y= -2log3(x-3) -1

Homework 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.

The Attempt at a Solution

Please instruct me on how to find logs on my calculator, thank you

 

[Ray Vickson]

Homework Statement

y= -2log3(x-3) -1

Homework 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.

The Attempt at a Solution

Please instruct me on how to find logs on my calculator, thank you

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.

 

[ilii]

sorry, it is the first expression you mentioned

 

[Mark44]

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

 

[Ray Vickson]

sorry, it is the first expression you mentioned

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##:
[tex] \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} [/tex]

 

[ilii]

ok thank you for the help everything is clear now