Help with exponents

[SourPatchParent]

I am trying to solve for "a" in:

16^(11a-1) = 128

I know the answer is a=1/4 but I haven't the slightest idea how to get to that answer--which isn't going to help me much in my future mathing experience.

If anyone can help it would be greatly appreciated,

Mel

 

[Steven G]

I am trying to solve for "a" in:

16^(11a-1) = 128

I know the answer is a=1/4 but I haven't the slightest idea how to get to that answer--which isn't going to help me much in my future mathing experience.

If anyone can help it would be greatly appreciated,

Mel

Replace 16 with 2^4 and 128 with 2^?. You can always use logs if you learned that method but it will be a longer process.

 

[SourPatchParent]

Replace 16 with 2^4 and 128 with 2^?. You can always use logs if you learned that method but it will be a longer process.

so (2^4)^(11a-1) = 2^7

...?

 

[Steven G]

so (2^4)^(11a-1) = 2^7

...?

Can you simplify this problem-- (5^2)^6. Write it in the form 5^(some number).

 

[SourPatchParent]

Can you simplify this problem-- (5^2)^6. Write it in the form 5^(some number).

5^12

 

[SourPatchParent]

5^12

2^4 x^(11a-1) =2^7

2^(4x11a-1) = 2^7

2^(44a-4) =2^(7+4)

2^44a = 2^11

2^(44a x 1/4) = 2^11

Thank you man for getting the gears going. If I did something wrong here please let me know.

 

[Steven G]

2^4 x^(11a-1) =2^7 No, 2^(4*(11a-1))

2^(4x11a-1) = 2^7 You did not distribute the 4! Should be 2^(44a-4)= 2^11

2^(44a-4) =2^(7+4) This does NOT follow from the previous line

2^44a = 2^11 What happened to -4 in the power 44a-4. If you do not change the RHS you can NOT change the LHS

2^(44a x 1/4) = 2^11 You changed the power in the LHS from the line above but did not change anything on the RHS

Thank you man for getting the gears going. If I did something wrong here please let me know.

Read comments above and answer these two questions. You also never answered the question by saying what a equals!
17^23 = 17^?
234^.45 = 234^?

 

[SourPatchParent]

Read comments above and answer these two questions. You also never answered the question by saying what a equals!
17^23 = 17^?
234^.45 = 234^?

I think I got a bit lazy with typing it out sorry, but this is everything I had written down. I hope this makes a bit more sense. Again, thank you for all your help. As for those two questions--I'm not quite sure I understand.

2^(44a-4) =2^7

2^(44a-4+4) = 2^(7+4)

2^(44a)= 2^11

2^(44a/44) = 2^(11/44)

2^a = 2^0.25

2^a = 2^(1/4)

a = 1/4

 

[Steven G]

I think I got a bit lazy with typing it out sorry, but this is everything I had written down. I hope this makes a bit more sense. Again, thank you for all your help. As for those two questions--I'm not quite sure I understand.

(44a-4) =7

(44a-4+4) = (7+4)

(44a)= 11

(44a/44) = (11/44)

a = 0.25 =1/4

2^a = 2^(1/4)

a = 1/4

You have the correct solution--good job! No need to keep writing the base 2. If you know that 2^a=2^(1/4) implies that a=1/4 then why can't you answer my exact same type problem??
if 17^23 = 17^?, then ?=23
if 234^.45 = 234^?, then ?=.45