Question

Find the value of x for which
\[\log_{2}(5.2^{x}+1),\log_{4}(2^{1-x}+1),1\] forms an A.P.

Answer 1

question is
log( 5.2^x +1) + log 2 = log (2^1-x +1)
where all bases are converted to 2
=> 5.2^(x+1) +2 = 2^(1-x) +1
=>10.2^(x) + 1 = 2/ 2^x

lets 2^x = y
it turns to be a quad eqn.
solve it..

Answer 2

how have you you changed the base of second term?

Answer 3

log a with base b = log a (base c) / log b (base c)

i just used this..

Answer 4

how?

Answer 5

RHS = log (2^1-x +1) base 4 = log (2^1-x +1) base 2 / log 4 base 2

clearer r?

Answer 6

am sorry my presentation might not seem nice,,hmm..