Solve Logarithmic Problem: Evaluate & Simplify

• lucky_star
In summary, the conversation is about a log problem and evaluating an expression using the laws of logarithms. The final answer is simplified to 3 divided by log2(10). The person asking for help is informed that their notation is incorrect and should be written as log2(10)/(1/3)*log2(10). They thank everyone for their help and acknowledge the need to pay more attention to proper notation in the future.
lucky_star
Hi, I have a log problem. Can anyone please check if I did it correctly!?

Homework Statement

Evaluate the following using the laws of logarithms.
These should be done without a calculator).

[log(5)+log(2)] / log2(cubic root of 10)
= log(5*2) / log2 (10)1/3
= log(10) / 1/3*log2(10)
= 3 / log2(10)

Is this simplified correctly? Can we simplify more?

Good.

Thank you!

Know this: Your notation is faulty near the end of your steps.

This, "= log(10) / 1/3*log2(10)" is not what you meant.
You really meant and should have written, log2(10)/(1/3)*log2(10)

That is because 1/ab is normally read as 1/(ab), not as (1/a) b.

Yes, that what I meant symbolipoint. Thank you everybody! I need to pay more attention on how I write it properly.

What is a logarithm?

A logarithm is the inverse function of exponentiation. In simpler terms, it is a way to express a number as the power to which another fixed number, called the base, must be raised to produce that number.

How do you solve a logarithmic problem?

To solve a logarithmic problem, you need to use the properties of logarithms to simplify the expression. This involves using rules such as the product rule, quotient rule, and power rule to manipulate the expression into a simpler form.

Why do we use logarithms?

Logarithms are useful in many scientific and mathematical applications. They can help us solve exponential equations, convert between different number systems, and measure the intensity of earthquakes and sound.

What is the difference between natural logarithms and common logarithms?

Natural logarithms have a base of e, which is a mathematical constant approximately equal to 2.718. Common logarithms have a base of 10. While both types of logarithms can be used to solve problems, natural logarithms are often used in calculus and other advanced mathematical concepts.

Can logarithms be negative?

Yes, logarithms can be negative. However, the base of the logarithm must be greater than 1 for the result to be negative. If the base is between 0 and 1, the logarithm will be positive. If the base is equal to 1, the logarithm will be undefined.

• Precalculus Mathematics Homework Help
Replies
8
Views
1K
• Precalculus Mathematics Homework Help
Replies
7
Views
2K
• Precalculus Mathematics Homework Help
Replies
5
Views
1K
• Precalculus Mathematics Homework Help
Replies
4
Views
1K
• Precalculus Mathematics Homework Help
Replies
4
Views
2K
• Precalculus Mathematics Homework Help
Replies
39
Views
2K
• Precalculus Mathematics Homework Help
Replies
10
Views
746
• Precalculus Mathematics Homework Help
Replies
3
Views
1K
• Precalculus Mathematics Homework Help
Replies
9
Views
2K
• Precalculus Mathematics Homework Help
Replies
5
Views
1K