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# Exponential and Logarithmic Functions

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1. Solve for x: ln(7x-1)=6

2. Solve for x: ln x = 3+ln(x-1)

3. The half-life of carbon-14 is 5730 years. Find the percent of a sample present after 5370 years. Answer: a.101.25% b.52.23% c.100.05% d.47.5%

4. If a principal of \$870 is invested at an annual interest rate of 4 percent compounded annually, which is the account balance at the end of 6 years?

5. Are the following function inverses of each other?
answer: yes or no a. F(x)=x-1/3 b. G(x)=3x-1

6. Identify the logarithmic expression written in exponential form. H=log29 g

7. Evaluate the expression: log5 25 answer: a.1/5 b.1/2 c.5 d.2

##### Solution Summary

Exponential and Logarithmic Functions are investigated.

Solution provided by:
###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

##### Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.