# How Do You Solve Logarithms with Square Roots?

• Antisubs12
In summary, the conversation revolves around solving logarithmic problems involving square roots, specifically the expression loge[square root of e]. The individual is seeking assistance in understanding how to approach these types of problems and a more efficient way of writing square roots in exponential form. Ultimately, they are able to figure out the solution with the help of the other person's advice.
Antisubs12
I've been working on logarithms in my calculus class and I came acrossed one with a square root. Since I am new to these types of problems I'm not sure how to work with this yet.

How would I solve something such as loge[square root of e]

Welcome to PF, Antisubs12.

Do you know another (equivalent) way to write

$$\log_{a}x^y = ?$$

Well, $\ln\sqrt{e}=\ln e^{1/2}=\frac{1}{2}\ln{e}=\frac{1}{2}$. Where the second equality comes from the rule ln(a)^b=b ln(a)

how would you write square root of e in expediential form? After you do that ask your self what law of logs will help you make the problem more workable.

ah thanks, i had forgotten there was a way to write square roots in exponential form. I can handle things from here. Thanks again.

## 1. What is a logarithm?

A logarithm is a mathematical function that represents the relationship between a base and its exponent. It essentially tells you how many times the base must be multiplied by itself to equal a given number.

## 2. Why are logarithms useful?

Logarithms are useful because they allow us to solve exponential equations and perform calculations involving very large or very small numbers. They also help us compare values that differ by orders of magnitude.

## 3. What is the difference between a log and a ln?

A log, or logarithm, is a function with a base of 10, while ln, or natural logarithm, is a function with a base of e (approximately 2.718). In other words, log is base 10 and ln is base e.

## 4. How do you solve a logarithmic equation?

To solve a logarithmic equation, you can use the properties of logarithms to rewrite the equation in a simpler form and then solve for the variable. Alternatively, you can convert the logarithmic equation into an exponential equation and solve for the variable.

## 5. What are the common uses of logarithms in science?

Logarithms are commonly used in science to measure the intensity of earthquakes, sound, and light, as well as to represent the pH scale for acids and bases. They are also used in biology to measure the loudness of sounds and the brightness of stars.

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