MORE ALGEBRA!! how do i solve 16^x = 2?

Question

there's a really easy way to do these but i don't remember..please show work

Answer 1

16 can be written as a power of 2.
16 = 2^4
Then
16^x
= (2^4)^x
= 2^(4x)

Also, 2 can be written as 2^1

So you have
2^(4x) = 2^1
When the bases are equal, then the exponents must be equal.
4x = 1
Divide both sides by 4
x = 1/4

Answer 2

that's a quadratic equation (a second degree polynomial with one variable x), the position one coefficient is an unknown consistent ok. So, use the quadratic formula ax^2 + bx + c = 0 a = 16 b = ok c = 16 x = [ -b +/- SQRT( b^2 - 4ac ) ] / 2a x = [ -ok +/- SQRT ( ok^2 - 4*16*16 ) ] / 32 x = [ -ok +/- SQRT(ok^2 - 1024) ] / 32 when you're operating with actual numbers, then the discriminant (the linked fee contained in the sq. root) can't be negative. If might want to be 0. if so, ok^2 = 1024, which makes ok = +/- 32 A discriminant = 0 signifies that the equation is a sq. (in ordinary words one root) if ok = +32, we get: 16x^2 + 32x +16 = 16(x+a million)(x+a million) = 0 this can in ordinary words be authentic if x = -a million If ok = -32, we get: 16x^2 - 32x +16 = 16(x-a million)(x-a million) = 0 this can in ordinary words be authentic if x = +a million --- If ok is better than +32 (or below -32), the discriminant is beneficial and, for each fee of ok, there'll be 2 roots (values of x the position the equation is an similar as 0)

Answer 3

you can rewrite the 16 as 2^4, to get 2^4x = 2^1

Since the exponetial function is one-to-one, you can say that this only happens when the exponents are equal, so we have 4x = 1, which means x = 1/4

Answer 4

16^x-2

Answer 5

by looking at it x=1/4

Answer 6

take log base 2 of each side:-
log2 (16^x) = 1
x log2(16) = 1
4x = 1
x = 1/4 = 0.25

Answer 7

If you have a graphing calculator, enter the left side and right side into y= and have the calculator find the point of intersection.

Answer 8

16^x = 2

log 16^x = log 2

x * log 16 = log 2

x = log 2 / log 16

Answer 9

ask a genus that's how u get the answer