If "2 raised to the power x plus 3 raised to the power x" is equal to 13, prove that x is equal to 2.

Question

2 exponent x + 3 exponent x = 13 ;

prove that x = 2

Answer 1

Note that x=2 is a solution.

f(x) = 2^x + 3^x is a continuous function of x.

Calculate f'(x) and show that it is positive everywhere. This proves that the function is monotonically increasing and therefore has at most one solution for a given value.

Answer 2

we know that:

if X = 3 then 2^3 + 3^3 = 35

if X = 1 then 2^1 + 3^1 = 5

also for X<1, 2^x + 3^x < 5

and for X>3, 2^x + 3^x > 35




It means:

the answer is Between 1 and 3.



you can see that the only answer is X = 2.

Answer 3

if 2 is raised to the second power (2x2) then it equal's 4. If 3 is reaised to the second power (3x3) then it equals 9.
Add them together and you have 13
2^2+3^2=13

Answer 4

2^x + 3^x is a strictly increasing function

2^2 + 3^2 = 13, and is the obvious solution
Since the function is increasing, only that one solution exists.

Answer 5

2^x=3 sq. the two aspects we can get : 2^(2x)=3^2=9 which means 2=9^(a million/2x) multiply by technique of two on the two aspects : 4=9^(a million/2x) * 2 which means : 4^(2x)=9 * 2^(2x)=9 * 9 (from 2d step) subsequently : 4^(2x) = 80 one