Which of the following best approximates the value of q if 6^44+3^11=6^q ?
Which of the following best approximates the value of q if 6^44+3^11=6^q ?
Answer/Solution
44
Steps/Work
We have: 6^44+3^11=6^q
==> because 3^11 > 0 --> 6^q MUST be equal or greater than 6^44 ==>q MUST be equal or greater than 44
==> Option E is out immediately.
Divide both sides by 6^q and q >= 44
We have:
6^(44-q) + 3^11/6^q = 1
Because q >= 44 ==>3^11/6^q = 0.0000xyz, that is very small,we can ignore it.
Thus, 6^(44-q) must be approximately 1
==> 44-q = 0 ==> q is approximately 44
D is the answer.
==> because 3^11 > 0 --> 6^q MUST be equal or greater than 6^44 ==>q MUST be equal or greater than 44
==> Option E is out immediately.
Divide both sides by 6^q and q >= 44
We have:
6^(44-q) + 3^11/6^q = 1
Because q >= 44 ==>3^11/6^q = 0.0000xyz, that is very small,we can ignore it.
Thus, 6^(44-q) must be approximately 1
==> 44-q = 0 ==> q is approximately 44
D is the answer.