Question

given that y+x=2 and 3^x=4^y . Show that x=1n16/1n12, and find y in a similar form.

Answer 1

xlog3 = ylog4

y = log3/log4 x

log3/log4 x + x = 2
x = 2/(1+log3/log4)
= 2/((log3+log4)/log4)
= 2/(log12/log4)
= 2log4/log12
= log16/log12

Now just solve for y in the same way