Question

log3 + log√3 9x = -2

Answer 1

hint : log√3 9x = log(3)^1/2 9x = log3 (9x)^2 = log3 81x^2

Answer 2

can u continue it

Answer 3

i got 1/81. it supposed to be 1/9. can u show me the calculation?

Answer 4

wait, is the log using 10 as the base ?

Answer 5

i think yes, so miss my the first hint (that was wrong)

Answer 6

okay. my bad,im sorry . the ques should be log (base=3) x + log (base=√3) 9x = -2

Answer 7

ah, still using my hint above :)

Answer 8

ok, now we have equation :
log3 x + log3 81x^2 = -2
simplify again, becomes
log3 (81x^2 * x) = -2
log3 (81x^3 ) = -2
convert to exponent form :
81x^3 = 3^-2 or
81x^3 = 1/9
x^3 = 1/(9 * 81)
x^3 = 1/729
x^3 = (1/9)^3
thus, the value of x = 1/9