Help with this math problem! Please!?

Question

log 10 of (x to the log 10 of x) = 4


( sorry, i didnt know how to use numbers to type it out)

Answer 1

Note that log[base 10] can simply be written as log. Let's omit the [base 10] part for that reason. After all, this is the way it is on the calculator.

log(x^(log(x))) = 4

By the log property log[base b](a^c) = c log[base b](a), we can move the log(x) in the exponent outside, giving us

[log(x)] [log(x)] = 4

Notice we have duplicate terms now, and we can write this as a square logarithm.

[log(x)]^2 = 4

Now we can take the square root of both sides. Note that when we do this, we have to insert a "plus or minus" symbol as per the usual method of taking square roots of both sides of an equation. This gives us

log(x) = +/- 2

This subsequently gives us two equations:
log(x) = 2, log(x) = -2. Solving them one at a time,

log(x) = 2. Converting this into exponential form,

10^2 = x, or x = 100.

log(x) = -2. Converting this into exponential form,
10^(-2) = x, or x = 1/100

Therefoure, our solutions are

x = {100, 1/100}

Answer 2

if I understand your question correctly then its:
log(x to the power of logx) = 4
so: (log x) squared = 4
log x = 2
log x = log 100
x = 100

Answer 3

Maybe you could upload a small picture of the assignment? Than you don't have to use all the numbers at all :)

Answer 4

10000 I think.