Logarithms and scientific calculator

In summary, the expression y= -2log3(x-3) -1 cannot be solved for x when x=3 because the logarithm does not exist.
  • #1
ilii
39
1

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
 
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  • #2
ilii said:

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.
 
  • #3
sorry, it is the first expression you mentioned
 
  • #4
If x = 3, then x - 3 = 0, so log3(x - 3) is undefined.
 
  • #5
ilii said:
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]
 
  • #6
ok thank you for the help everything is clear now
 

FAQ: Logarithms and scientific calculator

1. What are logarithms and how are they used in science?

Logarithms are mathematical functions that are used to express the relationship between numbers in an exponential form. In science, they are used to simplify complex calculations involving very large or very small numbers, as well as to convert between different units of measurement.

2. How do logarithms work?

Logarithms work by taking the exponent of a number and converting it into a coefficient. For example, the logarithm base 10 of 100 is 2, since 10 to the power of 2 is equal to 100. This allows for easier manipulation of large numbers and simplification of equations.

3. What is the difference between natural logarithms and common logarithms?

Natural logarithms, or ln, use the base e (approximately 2.718) and are commonly used in calculus and advanced mathematics. Common logarithms, or log, use the base 10 and are more commonly used in everyday calculations. Both can be used in scientific applications.

4. How can a scientific calculator help with logarithms?

A scientific calculator has special buttons or functions that allow for easy input and calculation of logarithms. These functions can also be used to calculate other mathematical operations such as exponents, roots, and trigonometric functions.

5. Can logarithms be negative?

Yes, logarithms can be negative. In fact, logarithms of numbers between 0 and 1 will result in negative values. However, the logarithm of 0 is undefined since there is no number that can be raised to a power to equal 0.

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