Question 836720
Your first equation and description do not match, so not sure what you really are given or want.


The next two are clearer, and help for them is next.



{{{ log( 10, x^logx ) }}} =4
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Show it this way:  {{{log(10,(x^log(10,x)))=4}}}, which looks like this, inside the braces tags:    log(10,x^log(10,x))=4

Since log((x)) is an exponent on x, we have a law of logarithms for this.
{{{(log(10,x))(log(10,x))=4}}}  
We obviously can take square root of both sides.
{{{log(10,x)=2}}}
Not even need calculator nor log tables.  Written in exponential form,
{{{highlight(10^2=x)}}}




{{{ log ( a,P ) }}} = .25 {{{ log ( a,y ) }}} + d
Solve for P.
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Express that equation cleanly using the system, this way:
{{{log(a,P)=0.25*log(a,y)+d}}}
Not too much you can do with this.  No given values or other relations for a, y, d.  All remaining to solve for P is put into exponential form.
{{{highlight(a^((1/4)log(a,y)+d)=P)}}}
OR
{{{highlight(P=a^(0.25*log(a,y)+d))}}}