How do you evaluate this log equation?

  • Thread starter haengbon
  • Start date
  • Tags
    Log
So your final answer should be -1.In summary, when simplifying the expression log39 + log41/64 + log51, you should first recognize that the second term can be rewritten as -log464 using the property of logarithms. Then, by combining like terms, the final answer is -1.
  • #1
haengbon
38
0

Homework Statement



log39 + log41/64 + log51


Homework Equations


none


The Attempt at a Solution



I tried answering it by...

(3x=9) + (4x=1/64) + (5x=1)
because of this, I got 5. Is that correct?
 
Physics news on Phys.org
  • #2
Hi haengbon! :smile:
haengbon said:
(3x=9) + (4x=1/64) + (5x=1)
because of this, I got 5. Is that correct?

Correct method :smile:, but wrong result :redface:

try (4x=1/64) again. :wink:
 
  • #3
tiny-tim said:
Hi haengbon! :smile:


Correct method :smile:, but wrong result :redface:

try (4x=1/64) again. :wink:

I tried it again and got -3 for 4x=1/64 :D is that correct now? ^^ thank you for the help by the way :)
 
  • #4
haengbon said:
I tried it again and got -3 for 4x=1/64 :D is that correct now? ^^

Yup! :biggrin:
 
  • #5
haengbon said:
I tried answering it by...

(3x=9) + (4x=1/64) + (5x=1)
because of this, I got 5. Is that correct?
If you turn in work like this, your instructor will probably deduct points, since you are apparently trying to add three equations.

Each of the log expressions is simple enough to calculate, so your work should look something like this.

log39 + log41/64 + log51
= 2 - log464 + 0
= 2 - 3 = -1

I used the fact that log(1/x) = - log(x) going from the first expression to the second.
 

FAQ: How do you evaluate this log equation?

1. What is a log equation?

A log equation is a mathematical expression that involves the logarithm function, which is the inverse of the exponential function. It is typically written in the form of logb(x) = y, where b is the base, x is the argument, and y is the logarithm.

2. How do you solve a log equation?

To solve a log equation, you can use the properties of logarithms, such as the power rule, product rule, and quotient rule. You can also convert the equation to exponential form, solve for the variable, and then convert back to logarithmic form if needed.

3. What are the common bases used in log equations?

The most commonly used bases in log equations are 10 (common logarithm), e (natural logarithm), and 2 (binary logarithm). However, any positive number can be used as a base for a log equation.

4. How do you evaluate a log equation?

To evaluate a log equation, you can plug in the given values for the base and argument into the logarithm function and use a calculator to find the result. You can also use the properties of logarithms to simplify the equation and then evaluate it.

5. What are the applications of log equations in science?

Log equations have various applications in science, such as in chemistry to calculate pH and in physics to model exponential growth and decay. They are also commonly used in data analysis and signal processing.

Back
Top