{x }^(2) = {16}^(x) find the value of x. show working please.​

Question

`{x }^(2) = {16}^(x)`
find the value of x.
show working please.​

Answer 1

You can solve this problem by inspection or by plotting.

x^2 = 16^x

x^2 = 2^(4x)

x = 2^(2x)

Take log of both sides:

logx = 2xlog2

(logx)/x = 2log2

x^(1/x) = 2^2

x^(1/x) = 4

Plot problem:

x = -.5

Test (-.5)^(1/-.5) = 4, 4 =4

(-.5)^2 = 16^(-.5)

1/4 = 1/4

Answer is: -.5