Help w/ 3 Exponential and Logarithmic Functions Problems

[edd fedds]

Really Need help on three problems on my study guide:

1.)If log.5 = -.3010, what is the mantissa of log.5?
a. 0
b. 1
c. .3010
d. .6990
*The mantissa is the number to the right of the decimal. So my answer was C. but since in the question there was a negative do I need to add a positive and a negative and multiply it by 10. Is C. the correct answer?

2.)Find the logarithm of 1500. Round the answer to four decimal places.
a. 3.1761
b. .1761
c. .1761 - 3
d. 1761
* When I put log(1500) I got 3.1761 which is choice A. Is choice A correct or is there more that I need 2 do?

3.)Solve the equation 7(x - 2) = 5x. Round the answer to four decimal places.
a. 8.3219
b. 9.6253
c. 10.1263
d. 11.5665
* When I solved I got 11.57 so would my answer be choice D. or did I miss something?

Please and Thank you very much! :mrgreen:

 

[masters]

Really Need help on three problems on my study guide:

1.)If log.5 = -.3010, what is the mantissa of log.5?
a. 0
b. 1
c. .3010
d. .6990
*The mantissa is the number to the right of the decimal. So my answer was C. but since in the question there was a negative do I need to add a positive and a negative and multiply it by 10. Is C. the correct answer?

Hi edd fedds,

The mantissa is defined as the positive fractional part. So the mantissa is .3010.

2.)Find the logarithm of 1500. Round the answer to four decimal places.
a. 3.1761
b. .1761
c. .1761 - 3
d. 1761
* When I put log(1500) I got 3.1761 which is choice A. Is choice A correct or is there more that I need 2 do?

Looks good to me.

3.)Solve the equation 7(x - 2) = 5x. Round the answer to four decimal places.
a. 8.3219
b. 9.6253
c. 10.1263
d. 11.5665
* When I solved I got 11.57 so would my answer be choice D. or did I miss something?

Please and Thank you very much! :mrgreen:

You lost me on this one. The solution here is 7. Did you mis-state the equation?

It doesn't appear to be logarithmic or exponential.

 

[edd fedds]

Thanx a bunch Masters. :mrgreen:
For the last question, I corrected the equation.
3.)Solve the equation 7^(x - 2) = 5x. Round the answer to four decimal places.
a. 8.3219
b. 9.6253
c. 10.1263
d. 11.5665
* When I solved I got 11.57 so would my answer be choice D. or did I miss something?
[None of the answer choices are 7, so how would I go about answering this question. I got 11.57 by using th natural logarithm (ln) in the equation. How did you get 7? [confused.]

 

[masters]

Thanx a bunch Masters. :mrgreen:
For the last question, I corrected the equation.
3.)Solve the equation 7^(x - 2) = 5x. Round the answer to four decimal places.
a. 8.3219
b. 9.6253
c. 10.1263
d. 11.5665
* When I solved I got 11.57 so would my answer be choice D. or did I miss something?
[None of the answer choices are 7, so how would I go about answering this question. I got 11.57 by using th natural logarithm (ln) in the equation. How did you get 7? [confused.]

Well, I'll tell you how I got 7.

Your original equation, before you corrected it was 7(x-2)=5x.

Now, if you solve that thing, x = 7. I assumed you mis-stated the equation since that wasn't one of your choices.

You re-stated the equation to 7^(x-2)=5x which is still wrong.

The equation should've been \(\displaystyle 7^{x-2}=5^x\).

Here's the solution:

\(\displaystyle 7^{x-2}=5^x\)

\(\displaystyle (x-2) \ln 7=x \ln 5\)

\(\displaystyle x \ln 7-2 \ln 7=x \ln 5\)

\(\displaystyle x \ln 7 - x \ln 5 =2 \ln 7\)

\(\displaystyle x(\ln 7-\ln 5)=2\ln 7\)

\(\displaystyle x=\frac{2 \ln 7}{\ln 7-\ln5}\)

\(\displaystyle x \approx 11.5665\)

 

[edd fedds]

Thanx and sorry. Thats how I got my answer at first. Just wanted to verify that I did it right but sorry about typing the equation wrong. Thanx again! :mrgreen: