Question

If 2ˣ . 9²ˣ⁺³ = 7ˣ⁺⁵, then x =
(a) 5 log 7 + 6 log 3/log 162 - log 7 (b) 5 log 7 + 6 log 3/log 162 + log 7
(c) 5 log 7 - 6 log 3/log 162 + log 7 (d) none of these

Answer 1

Answer:

taking log of both sides,

log[2^x.9^2x+3 = log (7^x+5)

xlog2 + (2x+3)log9 = (x+5) log7

xlog2 + 2xlog9 + 3 log9 = xlog7 + 5log7

xlog2 + 4xlog3 + 6 log3 = xlog7 + 5log7

xlog2 + 4xlog3 - xlog7 = 5log7-6log3

x(log2+4log3-log7) = 5log7 - 6 log 3

x = (5log7-6log3)/(log2+4log3-log7)

x= (5log7-6log3)/(log162-log7)