Thread: Log questions, DID THEM ALL, Just need to make sure there correct?

Hey guys I'm new here. How's everyone doing? I just finished doing a bunch of log problems. If you find any faults, please tell me. This test counts for a lot, and every correct answer is worth big.

I wrote out all the questions, and at the bottom of each I wrote my answers in bold. Please guide me guys. I need to ace this.

1-A bacteria divides into 4 new cells every 20 minutes. If the bacteria reproduces for x hours, find the
exponential equation that represents the increase in population as a function of time.

I found y= 12^x

2- Simplify:
A- (2/3)^2X+3 = (27/8)^3X-2
I found x=0,27

B- 3^x+3= 13574
I found x= 5.6617

3- Find the inverse of the following function: f (x)= log base5(3-x)
I found y= -5^x + 3

4- For the following function f(x)= 3 (1/2)^4x-1 + 5, State whether the statements are true or false. Correct the false ones.

A. It is decreasing
B. The ordinate is 8
C. The equation of the asymptote is y=5
D. It is always positive
E. It has no abcissa at the origin

I wrote true for A, C, D and E, and I wrote the ordinate is 11 for B

5- Find the equation of the following log function with an asymptote of x= -5.625 and passing through the point (10,3)
I found y= log2.5 (x+5.625)

6- Martha brought a bond for 1500.00$ at an annual rate of 4.8%, compounded semi annually. Find the rule that
describes the value as a function of the number of years. Using the rule, find the value in 10 years.

I found the rule was y= 1500. 1.024^2x, so in 10 years
y= 1500 . 1.024^20= 1901,47$

7- The following rule is used for calculating the number of years (y) it takes for a bond to reach a certain amount (x)
y= 96.64logx - 460.34
Calculate how much time it would take to reach 65000 and 85000.

I put in 65000 and 85000 for x, and got 4.78 and 16.04.

8. Find the value of the following expression:
8(log4 32 + log2 8) - (log2 16)^2

I found 28

Thanks in advance guys!

Originally Posted by helpmeplz

...
2- Simplify:
A- (2/3)^(2X+3) = (27/8)^(3X-2)
I found x=0,27

B- 3^(x+3)= 13574
I found x= 5.6617

...

All your considerations and calculations are OK!

You only should use brackets to make clear which term belongs to an exponent. (See coorections in red)