Exponents and Logs

Questions and Answers

- 1.
### Log

_{3}(1/27)Explanation

The expression log3(1/27) can be rewritten as log3(3^-3). Since log3(3^-3) is the exponent to which we need to raise 3 to obtain 3^-3, the answer is -3.Rate this question:

- 2.
### Log

_{8}2Explanation

8^x = 2

2^3x = 2^1

3x = 1

x = 1/3Rate this question:

- 3.
### Ln(e

^{4})Explanation

log base 3 of e^4 has to be 4.

e^x = e^4, so x = 4Rate this question:

- 4.
### Log

_{25}(1/5)Explanation

25^(1/2) is the sqrt of 25 = 5, to get it in the denominator, make the power negative.Rate this question:

- 5.
### Log

_{x}256=2Explanation

x^2=256

x=sqrt(256) = 16Rate this question:

- 6.
### Log(1/10,000)

Explanation

10^(-4) = 1/(10^4) = 1/10,000Rate this question:

- 7.
### What is the inverse of y = log

_{7}x?Use ^ to indicate an exponentExplanation

An exponential equation with the same base is the inverse of a logarithmic equation.Rate this question:

- 8.
### How much money did you invest compounded continuously if ended up with $1491.82 after 10 years at an interest rate of 4%?

Explanation

1491.82=Pe^(.04*10)

1491.82=P(1.49182)

P = 1000Rate this question:

- 9.
### How much more acidic is a liquid that is given a pH number of 2 than a pH number of 4?

Explanation

The difference in the exponents is 2 - that is 10^2 difference in acidity.Rate this question:

- 10.
### Where would the vertical asymptote of the graph y = log

_{3}(x - 4) be?Explanation

shift 4 units rightRate this question:

- 11.Explanation

216 = 6^3, so the fourth root of 216 = 6^(3/4)Rate this question:

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