Question 34026
<pre>
i am having a hard time answering these problems.

1. x=8log(100,10)

2. logx (1/16)=-2

3. log(x)=square root log(x)

The following has 2 solutions, not 1 (ONE)!
3. log(x)=square root log(x)
            {{{log ((x)) = sqrt(log ((x)))}}}
        {{{(log ((x)))^2 = (sqrt(log ((x))))^2}}} ----- Squaring both sides
        {{{(log ((x)))^2 = log ((x))}}} 
{{{(log ((x)))^2 - log ((x)) = 0}}} 
log (x)[log (x) - 1] = 0 ----- Factoring out GCF, log (x)
log (x) = 0        OR        log (x) - 1 = 0
log (x) = 0        OR        log (x) = 1
Converting to EXPONENTIAL form, we get:
{{{highlight(x) = 10^0 = highlight(1)}}}    OR   {{{highlight(x) = 10^1 = highlight(10)}}}</pre>