Hey everyone;

There are some questions on my review I am having trouble with.
4. Evaluate each logarithm.
g)log base 5 square root 5
I can't figure out how to do square roots...
h)log base 3 1
I got 3, but the anwser is 0

Also, directions ask you to write problems a) in exponential form and b) in logarithmic form. This is a really stupid question, but what exactly is the difference?

Any help is appreciated so much!
Thanks!

Hi there! I'm here to help you with your questions. Let's start by addressing your concerns about logarithms and square roots.

To evaluate the logarithm, g) log base 5 of square root 5, we can rewrite it using the property of logarithms: log base b of x = y is equivalent to b^y = x. In other words, logarithms and exponents are inverse operations.

In this case, we want to find a number y such that 5^y = √5. Since the square root is the same as raising a number to the power of 1/2, we rewrite this equation as 5^y = 5^(1/2).

To solve for y, we set the exponents equal to each other: y = 1/2. Therefore, the value of the logarithm log base 5 of square root 5 is 1/2.

Moving on to h) log base 3 of 1. In logarithmic form, this means log base 3 of x = 1. To evaluate the logarithm, we need to find a number x such that 3^1 = x. Since any number raised to the power of 1 equals itself, we have x = 3.

Now, let's address your question about the difference between exponential and logarithmic formulas.

In exponential form, a number is written as a base raised to an exponent. For example, 2^3 = 8. The base is 2, the exponent is 3, and the result is 8.

In logarithmic form, we commonly use the logarithm with a specific base to represent the exponent that produces a given result. For example, log base 2 of 8 = 3. The base is 2, the result is 8, and the logarithm gives us the exponent, which is 3 in this case.

To convert from exponential to logarithmic form, you simply state the base, the result, and the exponent. In our example, 2^3 = 8 becomes log base 2 of 8 = 3.

To convert from logarithmic to exponential form, you state the base, the exponent, and the result. For example, log base 2 of 8 = 3 becomes 2^3 = 8.

I hope this explanation clarifies things for you! Let me know if you have any more questions.