# Evaluating Logs & Derivatives: More Questions Answered Here

• m0286
In summary, the conversation includes requests for help in solving logarithm questions and determining the derivative of two equations. The specific questions mentioned are evaluating log22^log55, log25=log2(x+32)-log2x, and determining the derivative of y=2x^3 e^4x and y=square root(x^3 + e^-x + 5). The conversation ends with a question about the notation in part a of the problem.
m0286

I have a couple more log questions I am stuck on. They keep giving me log questions that they never showed me how to do.. very fustrating!
I need to evaluate the following logarithms:

68 a). log22^log55
I don't even know where to begin.. I never done a log with an exponent log?

69. log25=log2(x+32)-log2x

Determine the derivative of:
70 c) y= 2x^3 e^4x

e) y= square root(x^3 + e^-x +5)
I know this one should probably go to. (x^3 + e^-x +5)^1/2... then,
dy/dx= (x^3 + e^-x +5)^1/2 * 1/2(x^3 + e^-x +5)^-1/2 * (3x^2)now I am confused? does the e^-x have a derivative?? like -xe^-2?? i got no idea.
THANKZ YA!

Last edited:
For part a, is that

$$(\log_{2}2)^{\log_{5}5}$$ or $$\log_{2}(2)^{\log_{5}5}$$?

umm there are no brackets, but i think the 2 is in part with the log2

Hrm

$$\log_{5} 5 = 1$$

$$5^1 = 5$$

$$log_{2} 5= log_{2} (x+32) - log_{2} x$$

$$log_{2} 5= log_{2} \frac{x+32}{x}$$

$$5 = \frac{x+32}{x}$$

Last edited:

## 1. What is the purpose of evaluating logs and derivatives?

The purpose of evaluating logs and derivatives is to calculate the rate of change of a function or the slope of a curve at a specific point. This is useful in many areas of science, such as physics, engineering, and economics.

## 2. What are the key concepts of evaluating logs and derivatives?

The key concepts of evaluating logs and derivatives include the power rule, product rule, quotient rule, and chain rule. These rules allow us to find the derivative of more complex functions by breaking them down into simpler parts.

## 3. How do you find the derivative of a logarithmic function?

To find the derivative of a logarithmic function, you can use the power rule or the logarithmic differentiation method. The power rule states that the derivative of logb(x) is 1/(xln(b)). The logarithmic differentiation method involves taking the natural logarithm of both sides of the function and then differentiating using the rules of logarithms.

## 4. What is the relationship between logs and exponents?

The relationship between logs and exponents is that they are inverse functions of each other. This means that if logb(x) = y, then by = x. In other words, logs tell us what exponent we need to raise the base to in order to get a certain number.

## 5. How are logs and derivatives used in real-world applications?

Logs and derivatives are used in many real-world applications, such as in finance to calculate interest rates, in physics to find the velocity and acceleration of a moving object, and in biology to model population growth. They are also used in data analysis to find patterns and trends in large datasets.

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