Question 1012454
Good evening, I have some difficulties with this logarithmic equation:
4log4((x+1)^(1/2)) - log2(5-7x)=0
I tried to solve changing the base in such a way:
4log4((x+1)^(1/2)) = (log4(5-7x))/log4(2)
but I do wrong somewhere solving the arguments.
Can somebody help me explaining the right method?
Many thanks  
<pre>{{{4 * log (4, (x + 1)^(1/2)) - log (2, (5 - 7x)) = 0}}}
{{{4 * log (4, (x + 1)^(1/2)) = log (2, (5 - 7x))}}} ---- Adding {{{log (2, (5 - 7x))}}} to both sides
{{{(1/2) * 4 * log (4, (x + 1)) = log (2, (5 - 7x))}}} --- Applying {{{a * log (b, c^d) = ad * log (b, c))}}} 
{{{2 * log (4, (x + 1)) = log (2, (5 - 7x))}}} 
{{{2 * log (2, (x + 1))/log (2, 4) = log (2, (5 - 7x))}}} ------- Applying change of base to {{{log (4, (x + 1))}}}, to base 2
{{{2 * log (2, (x + 1))/2 = log (2, (5 - 7x))}}} ------- Changing {{{log (2, 4)}}} to 2
{{{cross(2) * log (2, (x + 1))/cross(2) = log (2, (5 - 7x))}}} ------ Cancelling 2 in numerator and denominator
{{{log (2, (x + 1)) = log (2, (5 - 7x))}}}</pre><pre>x + 1 = 5 - 7x 
x + 7x = 5 – 1
8x = 4
x = {{{4/8}}}, or {{{highlight_green(x = 1/2)}}}