Question 1095566
Hi, I'm tried to solve these problems but I'm having trouble:

1) If loga(x) = 0.6 and loga(y) = 0.2, evaluate loga(x^2/square root y) - I don't know how to express loga(y) as a square root.

What I have tried: loga(x) + loga(x) - loga(square root y)

2) loge(x) - 3 = loge(square root x).....when x>0

Thankyou in advance.
<pre><b>1)</b>   {{{matrix(1,3, log (a, (x)), "=", 0.6)}}}            {{{matrix(1,3, log (a, (y)), "=", 0.2)}}}

     {{{log (a,  x^2/sqrt(y))}}}
     {{{log (a, (x^2)) - log (a, (sqrt(y)))}}}
     {{{2 * log (a, (x)) - matrix(2,1, "", log (a,  (y^(1/2))))}}} 
     {{{2 * log (a, (x)) - (1/2) * log (a, (y))}}}
     {{{2(0.6) - (1/2)(0.2)}}} ------ Substituting {{{matrix(1,7, 0.6, for, log (a, (x)), and, 0.2, for, log (a, (y)))}}} 
     {{{highlight_green(matrix(1,3, 1.2 - 0.1, "=", highlight(1.1)))}}}</pre>
<pre><b>2)</b>  {{{matrix(1,3, log (e, (x)) - 3, "=", log (e, (sqrt(x))))}}}
     {{{matrix(1,3, log (e, (x)) - log (e, (sqrt(x))), "=", 3)}}}
     {{{matrix(1,3, log ((e), (x/matrix(2,1, "", x^(1/2)))), "=", 3)}}}
     {{{matrix(1,3, matrix(2,1, "", log (e, (x^(1/2)))), "=", 3)}}}
     {{{matrix(1,3, matrix(2,1, "", x^(1/2)), "=", e^3)}}} ----------- Converting to EXPONENTIAL form 
     {{{matrix(1,3, (x^(1/2))^2, "=", (e^3)^2)}}} ---- Squaring both sides
     {{{highlight_green(matrix(1,5, x, "=", e^6, "=", highlight(403.429)))}}}</pre>