Question

Which of the following is the solution to the equation 25^(z + 2) = 125 ?

z = 5.5

z = 3.5

z = –2.5

z = –0.5

Answer 1

Take the natural log of the equation.
HINT: \[\ a^n=ln (a)^n = n \ln(a)\] where 'a' is a constant.

Answer 2

Then, use algebra to rearrange and solve for z.

Answer 3

Could you work through the steps for me?

Answer 4

please?

Answer 5

I gave you a good amount of tip and hints. Try and work it out yourself first. If you are wrong, there are no penalties. I will help guide you in the right direction.

Answer 6

z= 5.5 ?

Answer 7

Am I right?

Answer 8

?

Answer 9

Not quite. How did you get that?

Answer 10

well I got down to z= 11/2

Answer 11

Your first step should be to take the natural log of everything and take the form:
\[(z+2)\ln25 = \ln125\]

Answer 12

Your next step should be to divide by...

Answer 13

1n25 ? since its outside the parenthesis?

Answer 14

Correct! Now you have:
\[z+2 = \frac{ \ln125 }{ \ln25 }\]

Answer 15

Now, what can you do next to solve for z?

Answer 16

add 2 to each side

Answer 17

Well, not add 2, but instead subtract. If you add 2 to both sides, you get z+4, and you're solving for z = #

Answer 18

oh, what do we do from there?

Answer 19

Subtract 2 from both sides and thats your answer. Plug it into a calculator to get your answer.

Answer 20

z= -2.5 ?

Answer 21

?

Answer 22

hello can someone confirm this???????????????????????????????????

Answer 23

\[25=5^2\]
\[125=5^3\]

Answer 24

\[25^{z+2}=5^{2z+4}=5^3\]
\[2z+4=3\]
\[2z=-1\]
\[z=-\frac{1}{2}\]

Answer 25

i have no idea what that log stuff was about, it is totally unnecessary

Answer 26

thanks, that makes more sense to me lol

Answer 27

Idk, I got -0.5 using log. Lol