Evaluating logarithms given log(a)b = 3

  • Thread starter zebra1707
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    Logarithms
In summary, the conversation discusses a student's attempt to evaluate a logarithmic expression using the properties of logs. The student correctly simplifies the expression and reaches the correct answer of 6. They also mention the rules they used to solve the problem.
  • #1
zebra1707
107
0
Hi there

Can someone please review my work and advise.

Homework Statement



Given log(a)b=3 , use the properties of logs to evaluate

4log(a)(1/b)+2log(a)b^3

Homework Equations



I used the rules

log(a)1 = 0

log(a)(x/y) = log(a)x-log(a)y

log(a)x^m = mlog(a)x

The Attempt at a Solution



=4loga1-4logab+2logab^3
=-12+6*3
=-12+18
=6
 
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  • #2
zebra1707 said:
Hi there

Can someone please review my work and advise.

Homework Statement



Given log(a)b=3 , use the properties of logs to evaluate

4log(a)(1/b)+2log(a)b^3

Homework Equations



I used the rules

log(a)1 = 0

log(a)(x/y) = log(a)x-log(a)y

log(a)x^m = mlog(a)x

The Attempt at a Solution



=4loga1-4logab+2logab^3
=-12+6*3
=-12+18
=6
That is correct !
 
  • #3
SammyS said:
That is correct !

Thank you for your assistance.
 

1. What is a logarithm?

A logarithm is a mathematical function that is the inverse of exponentiation. It tells us what power we need to raise a specific number (called the base) to in order to get another number. For example, in the equation log2(8) = 3, the base is 2, and the logarithm tells us that 2 to the power of 3 equals 8.

2. What does log(a)b = 3 mean?

This equation is read as "log base a of b equals 3". It means that the logarithm of b with a as the base is equal to 3.

3. How do you evaluate logarithms given log(a)b = 3?

To evaluate this logarithm, we need to find the value of b. This can be done by taking the base a to the power of 3, since that is the value of the logarithm. In other words, b = a3.

4. Can this equation be solved for a if log(a)b = 3?

Yes, this equation can be solved for a. We can rewrite the equation as a = b1/3, which means that a is equal to the cube root of b.

5. What are some practical applications of evaluating logarithms?

Logarithms are commonly used in fields such as science, engineering, and finance. They can help us solve exponential growth and decay problems, calculate pH and sound intensity, and analyze data on a logarithmic scale. In the context of evaluating log(a)b = 3, it can help us find the unknown variable b in equations involving exponential functions.

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