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\[ If \, 8^{13}=2^z , then \, z= \]

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by VJesus12 » Fri Apr 27, 2018 1:06 am
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$$If\ \ \ 8^{13}=2^z,\ then\ z=\ $$

(A) 10
(B) 13
(C) 19
(D) 26
(E) 39

The OA is the option E.

What are the calculations I should do here? I need some help please.
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by Vincen » Fri Apr 27, 2018 3:18 am
Hi Vjesus12.

Here we just need to use the properties of the powers as follows: $$8^{13}=2^z\ \ \ \Leftrightarrow\ \ \ \left(2^3\right)^{13}=2^z\ \ \ \Leftrightarrow\ \ 2^{39}=2^z\ \ \ \Leftrightarrow\ \ z=39.$$ Thus, the correct asnwer is the option E.

I hope it helps.
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by Brent@GMATPrepNow » Fri Apr 27, 2018 6:24 am
VJesus12 wrote:$$If\ \ \ 8^{13}=2^z,\ then\ z=\ $$

(A) 10
(B) 13
(C) 19
(D) 26
(E) 39
GIVEN: 8^13 = 2^z
We want to rewrite our powers so that they have the SAME BASE

Rewrite 8 as 2^3 to get: ( 2^3)^13 = 2^z
Simplify left side to get: 2^39 = 2^z
So, it must be the case that 39 = z

Answer: E

Cheers,
Brent
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by Scott@TargetTestPrep » Mon Apr 30, 2018 3:40 pm
VJesus12 wrote:$$If\ \ \ 8^{13}=2^z,\ then\ z=\ $$

(A) 10
(B) 13
(C) 19
(D) 26
(E) 39

We can re-express 8 as 2^3. Substituting into the equation and simplifying, we have:

(2^3)^13 =2^z

2^39 = 2^z

Recall that when the bases are equal, the exponents are equal. Thus, we have:

39 = z

Answer: E

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