Question

Solve the equation

Answer 1

\[(lgx)^{lgx}=x\]

Answer 2

I can only suggest you graph y = (lgx)^(lgx) and y = x and see if they intersect.

Answer 3

https://www.desmos.com/calculator/1dbqsre8am

It might look if x = 1 is a solution but it isn't because log 1 ^ log 1 = 0^0 is indeterminate

Answer 4

So there is no solution.

Answer 5

Ah, thank you!

Answer 6

@welshfella can you help me with this one too?

\[(\log_{5} x)^2-3\log_{5} (x+2)=0\]

Answer 7

convert to natural logarithms

ln^2 x ln (x+2)^3
------ = -------
ln^2 5 ln 5

Answer 8

1.6094 ln^2 x = 2.5903 ln (x + 2)^3

ln^2 x = 1.6095 ln (x + 2)^3

again you can solve this one graphically

use desmos.

Answer 9

to convert to natural logs I used the change of base rule;

logb x = loga x / loga / b