Question

Find all numbers x such that \[x + 3^x \lt 4\]Find all numbers x such that \[x + 3^x \lt 4\]@Mathematics

Answer 1

I'm stuck on this one and the next few... :(

Answer 2

notice that when x=1
\[x+3^x=4\]

Answer 3

yeah, but what if I don't notice?

Answer 4

like in the next few questions?

Answer 5

if you had something other than 4 you would probably have to solve numerically.

Answer 6

graph them. it's true for x < 1

Answer 7

graph y = x + 3^x and y = 4

Answer 8

no graphing calculators existed in 1969

Answer 9

you don't need a calculator to draw those two graphs

Answer 10

well..... I don't want to use graphs because we are still using just numbers

Answer 11

i see no way of solving 3^x + x = 4 by elementary methods. simply guessing x = 1 is the only way.

you could possibly use Lambert W function

Answer 12

I guess I'll have to use what works then :-(

Answer 13

sorry agdgdgdgwngo i have one more problem for you to answer plz help me???

Answer 14

x = 4 + W/ln(3), where W = Lambert(3^-4/ln(3))

= 1

Answer 15

x = 4 + W/ln(3), where W = Lambert(1/(27ln(3)))

= 1

Answer 16

oops:

x = 4 + W/ln(3), where W = Lambert(1/(81ln(3)))

= 1

Answer 17

oops got it wrong again:

3^x + x = 4

3^x = 4 - x

(4 - x)*3^(-x) = 1

Let m = 4 - x, then x = 4 - m

m * 3^(m-4) = 1

thus m * 3^(m) * 3^(-4) = 1

thus m * 3^m = 81

so m * e^(ln(3)*m) = 81

so ln(3)*m * e^(ln(3)*m) = 81*ln(3)

hence ln(3)*m = W(81*ln(3))

thus m = W(81*ln(3))/ln(3)

thus x = 4 - W(81*ln(3))/ln(3), where W(x) is Lambert W function

= 1