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

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

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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Source: Beat The GMAT — Problem Solving | Fri Apr 27, 2018 1:06 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8188; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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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