Question 1061117

Given log3(8)=x and log4(7)=y express log27(14) in terms of x and y
<pre>{{{log (3, 8) = x}}} ======> {{{matrix(1,9, x, "=", log (8)/log (3), "=", log ((8)) - log ((3)), "=", log ((2^3)) - log ((3)), "=", 3 * log ((2)) - log ((3)))}}} ======> {{{matrix(1,3, log ((3)), "=", 3 * log ((2)) - x)}}} 
{{{log (4, 7) = y}}} ======> {{{matrix(1,9, y, "=", log (7)/log (4), "=", log ((7)) - log ((4)), "=", log ((7)) - log ((2^2)), "=", log ((7)) - 2 * log ((2)))}}} =======> {{{matrix(1,3, log ((7)), "=", y + 2 * log ((2)))}}}


{{{log (27, (14))}}} =======> {{{log ((14))/log ((27))}}} ======> {{{log ((14)) - log ((27))}}} =======> {{{log ((2 * 7)) - log ((3^3))}}} =======> {{{log ((2)) + log ((7)) - 3 * log ((3))}}}
{{{matrix(1,3, log (27, (14)), "=", log ((2)) + y + 2 * log ((2)) - 3 * (3 * log ((2)) - x))}}} ----- Substituting y + 2 * log (2) for log (7), and 3 * log (2) - x for log (3)
{{{highlight_green(matrix(1,9, log (27, (14)), "=", log ((2)) + y + 2 * log ((2)) - 9 * log ((2)) + 3x, "========>", log ((2)) + 2 * log ((2)) - 9 * log ((2)) + y + 3x, "=======>", y + 3x - 6 * log ((2)), or, y + 3x - 1.806179974))}}}