exponents

[Shoppingal]

4^2x =2^16
4^2x = 2^2^(16)
2x = 2(16)
2x/2 = 32/2
x=16

the answer is 4 but I'm not getting 4 can someone please show me where I went wrong

thanks

 

[pka]

4^2x =2^16
4^2x = 2^2^(16)
2x = 2(16)
2x/2 = 32/2
x=16
the answer is 4 but I'm not getting 4 can someone please show me where I went wrong

\(\displaystyle 4^{2x}=2^{4x}=2^{16}\)

 

[Deleted member 4993]

4^2x =2^16
4^2x = 2^2^(16) .............. How is that? that should be 4^(2x) = 2^[2^4]....... but follow pka's method (much simpler!)
2x = 2(16)
2x/2 = 32/2
x=16

the answer is 4 but I'm not getting 4 can someone please show me where I went wrong

thanks

.

 

[mmm4444bot]

4^(2x) = 2^16

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

please show me where I went wrong

If we raise the number 2 to the power of 2^16, we do not get 2^16 for the result.

In other words, you implied above that 2^16 = 2^2^16, and that's not true.

---

PS: Kindly note the red grouping symbols that I inserted. (Also, I do not understand why you put those symbols around 16. They don't mean anything.)

It's very important when texting math expressions to indicate any changes to the established Order of Operations.

When you type 4^2x it means \(\displaystyle 4^{2} \cdot x\)

Typing 4^(2x) instead means \(\displaystyle 4^{2x}\)


Have we already told you this in any of your other threads?

 

[Shoppingal]

Thank you for your help, and no you never mentioned anything in previous threads about the way it should be
represented. I appreciate all the help I am receiving from this site as I have recently returned to school after
many years and have found the math challening at best.

 

[HallsofIvy]

Thank you for your help, and no you never mentioned anything in previous threads about the way it should be
represented.

What mmm4444bot is talking about are not conventions for representing things on this board. The use of parentheses and order of operations are standard conventions for representing formulas in mathematics. You cannot write mathematics without them.