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.
\[ If \, 8^{13}=2^z , then \, z= \]
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GIVEN: 8^13 = 2^zVJesus12 wrote:$$If\ \ \ 8^{13}=2^z,\ then\ z=\ $$
(A) 10
(B) 13
(C) 19
(D) 26
(E) 39
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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Scott@TargetTestPrep
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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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