I have to take an assessment tomorrow with NO calc allowed. How do you do 16^x=3 = 64 ?

Question

We have a huge packet of stuff from 9th grade (I'm a soph in college) and I remember most of it.. I just forgot how to do these and a few other things. Thanks

im sorry. I meant x - 3

Answer 1

(2^4)^(x - 3) = 2^6
2^(4x - 12) = 2^6
4x - 12 = 6
4x = 18
x = 4½

Answer 2

Hey there!

Here's the answer.

16^(x-3)=64 --> Write the problem.
4^(2(x-3))=64 --> Rewrite 16 as 4^2.
4^(2(x-3))=4^3 --> Rewrite 64 as 4^3.
2(x-3)=3 --> Use the formula if a^x=a^y, then x=y.
2x-6=3 --> Distribute 2 into x-3.
2x=9 --> Add 6 to both sides of the equation.
x=9/2 --> Divide 2 on both sides of the equation.
x=4.5 Simplify 9/2.

So the answer is x=4.5.

Hope it helps!

Answer 3

I think its 16^(x-3) = 64.
Just like what is done earlier... convert them to a similar base...
§
16^(x-3) = 64
(4^2)^(x-3) = 4^3
4^(2x-6) = 4^3

then the rule is a^b = a^c , then b = c

thus 2x - 6 = 3
2x = 9
x = 9/2.

Well... if its 16^(x+3) = 64 ... adjust accordingly... just change the appropriate sign...

Answer 4

I assume you mean:

16^(x - 3) = 64

16 = 2^4
64 = 2^6

So we have:

16^(x - 3) = 64
(2^4)^(x - 3) = 2^6
2^[4(x - 3)] = 2^6

Since both sides are powers of 2, set the exponents equal.

4(x - 3) = 6
x - 3 = 6/4 = 3/2
x = 9/2

Answer 5

16^(x-3) = 64?

16 = 2^4
16^(x-3) = 2^(4(x-3))

64 = 2^6

4(x-3) = 6
x-3 = 3/2
x = 9/2

16^(9/2 - 3) = 64

Answer 6

The easiest way: 3x10 + 3x6 = 30 + 18 = 48

Answer 7

16^(x-3) = 64, is this what you want?
2^(4x-12) = 2^6
4x-12 = 6
x = 9/2
--------
Ideas: 16 = 2^4 and 64 = 2^6

Answer 8

First of all, what you wrote makes no sense. You've got one too many equals signs there. What is the actual equation you're trying to solve?

Answer 9

what? 3 does not equal 64, so I think you typed something wrong.