Question 1057131
I just need someone to explain this and why 2 is the answer:
3^(log base 9 (4))= 2

I'm not sure how to write out log base correctly, but it's log(4) with the base of 9.
<pre>{{{3^(log (9, (4)))}}}
Let {{{3^(log (9, (4))) = x}}}
{{{log (3, (x)) = log (9, (4))}}} ------- Converting from EXPONENTIAL to LOGARITHMIC form
{{{log (3, (x)) = log (3, (4))/log(3, (9))}}} ------- Changing right side to base 3, by applying CHANGE OF BASE
{{{log (3, (x)) = log (3, (4))/2}}} ------- Changing {{{log (3, (9))}}} to 2
{{{2 * log(3, (x)) = log (3, (4))}}} ----- Cross-multiplying
{{{log (3, (x)^2) = log (3, (4))}}} ------ Applying {{{a * log (b, (c)) = log (b,(c)^a)}}} to left-side of equation
{{{x^2 = 4}}} ------ Equating expressions since log bases are the same
{{{highlight_green(matrix(1,9, x, "=", sqrt(4), or, x,  "=", 2, "=", 3^(log (9, (4)))))}}}