Question 260352
Here is the original problem
(i) {{{9log(27,x) - 4log(9,x) }}}
Here are the step I took:
step 1 - write {{{9log(27,x) = Y}}} and solve for Y
{{{27^Y = x^9}}}
{{{(3^3y) = x^9}}}
taking a log base 3 of both sides, we get
{{{3y = log(3,x^9)}}}
{{{y = (9/3)log(3,x) = 3log(3,x)}}}
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step 2 - write {{{4log(9,x) = Z}}} and solve for Z
{{{9^Z = x^4}}}
{{{(3^2Z) = x^4}}}
taking a log base 3 of both sides, we get
{{{2Z = log(3,x^4)}}}
{{{y = (4/2)log(3,x) = 2log(3,x)}}}
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step 3 - rewriting steps 1 and 2, we get
{{{3log(3,x) - 2log(3,x)}}}
which is simply
{{{log(3,x)}}}