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

Question

turingtest · Answer

rewrite 25 and 125 as powers of 5, and apply the rule$$\large (x^a)^b=x^{ab}$$then both sides will have the same base, which you can take the logarithm of

anonymous · Answer

i have no idea how to do it at all

turingtest · Answer

$$\large25=5^?$$

turingtest · Answer

i.e. 25 is 5 raised to what power?

anonymous · Answer

second

turingtest · Answer

good
what about 125 ?

anonymous · Answer

5^3?

turingtest · Answer

yep :)
so now we have$$\large(5^2)^{z-2}=5^3$$now we use the log rule I stated above$$\large(x^a)^b=x^{ab}$$to get$$\large5^{2z-4}=5^3$$make sense?

anonymous · Answer

yes but i dont understand how to get the answer. is it -.5?

turingtest · Answer

no...
to get the final answer take the log base 5 of both sides, then solve the resulting (linear) equation for x
if this is a novel concept to you then you must have missed a lot...

anonymous · Answer

yea i was going thru alot at home and missed a lot of school ://

so the 2z-4 =3?