Solve for x in 4 ^2x-3 = 16?

Question

anonymous · Answer

$$4^{2x-3} =16$$

mimi_x3 · Answer

Ok lets convert 16 into a base of 4
we know that $ 4^2=16$
So $$4^{2x-3}=4^2$$

mimi_x3 · Answer

So if  $$4^{2x-3}=4^2$$
 Then obviously the 2 exponents equal each other so 
2x-3=2

Do you follow?

anonymous · Answer

yes

mimi_x3 · Answer

SO now solve for x

anonymous · Answer

x = -1/2?

mimi_x3 · Answer

2x-3=2
2x=5 ....

anonymous · Answer

oh sorry i messed up on the charge and then you divide by two so x would be 5/2

mimi_x3 · Answer

yup yup
Medal +Fan

anonymous · Answer

okay can you help me with another one?

mimi_x3 · Answer

Sure go for it

anonymous · Answer

$$2^{x^2+2x-3} = 1$$

mimi_x3 · Answer

Ok we know that $y^0=1$ Meaning any number to the power of 0 equals 1
The exception to this rule is $0^0=0$
So now in order to solve for x  we want both sides to have the same base
so how can we write 1 with a base of 2?????
Well $2^0=1$
So $$2^{x^2+2x-3}=2^0$$
Can you take it from here?

anonymous · Answer

so would it be x^2 + 2x -3

mimi_x3 · Answer

$$x^2+2x-3=????$$

anonymous · Answer

2?

mimi_x3 · Answer

hmmm we are equating the exponents of either side of the equal sign since they both have the same base  - a base of 2
So noooo it doesnt equal 2

anonymous · Answer

so then its 0?

mimi_x3 · Answer

Yes
$$x^2+2x-3=0$$
We now can factor and solve for x
We will have 2 solutions for x

anonymous · Answer

do we factor it?

anonymous · Answer

would it be (x-1)(x-2)

mimi_x3 · Answer

We are dealing with quadratics sooo ...
Im lazy to start explaining quadratics rn 
You familiar with this ??? 
(x-s)(x-r)=0
So x=s and r

mimi_x3 · Answer

Pretty close

mimi_x3 · Answer

ax^2+bx+c=0
a=1
b=2
c=-3
We need two numbers that when you add them equal 2 and when you multiply them you get -3

abb0t · Answer

Why don't you take the natural log of both sides to make it easier.

mimi_x3 · Answer

ya it wld buttt ... not sure what this b!tch of a hs teacher wants

mimi_x3 · Answer

Im almost positive they want same bases cuzz it keeps working out perfectly

anonymous · Answer

i think they actually want the natural log but i don't care i just want the answer i still have 20 more questions to do

anonymous · Answer

lol

abb0t · Answer

Knew it. You're a cheater.

mimi_x3 · Answer

Ohhh so take natural log if ya want ....
But ya u shld know how to factor lmao

abb0t · Answer

This is a place to help, not to give answers!

mimi_x3 · Answer

lmaooo  abbot stopppppp I need to get to beddddddddd

anonymous · Answer

i just get confused on which you add to and which you multiply too.

anonymous · Answer

how am i a cheater.. I'm doing the work out right? the that doesn't make me a cheater a cheater would be googling the fluttering answers, you don't like me asking for help? then block me and get off my page

anonymous · Answer

so it would be (x+1)(x-3)

mimi_x3 · Answer

Ok so any 2 numbers that when you add equal 2 and when you multiply equal -3
SO what are the factors of -3 ????
Only 1 and 3 obv
so -1*3=-3
and 3-1=2

anonymous · Answer

so just switch the positive and negative around from 1 to 3 right?

mimi_x3 · Answer

umm no its (x-1)(x+3)=0
Hence x=1 or -3

anonymous · Answer

yeah that what I meant because before i put (x+1)(x-3)

mimi_x3 · Answer

ohh gotcha so yaaaa u are correct

mimi_x3 · Answer

FAN ME PLSSSS

anonymous · Answer

thank you for your help and I will

anonymous · Answer

I fan'd you (:

anonymous · Answer

goodnight!

mimi_x3 · Answer

Thanks good night :D