Question

Ive been staring at this problem for like a half hour now and I cant figure out where to even begin...

log(base x)4 + log(base 8)squareroot(x) = 4/3

solve for x

any help appreciated

Answer 1

Have you come across the property

log_ab = log b/log a ?

log_x4 + log₈squareroot(x) = 4/3

log_x4 + (1/2)log₈(x) = 4/3

log4/logx + (1/2)logx/log8 = 4/3
let logx = t
log4/t + t/(2log8) = 4/3

multiply each term by (6log8)t to get the quadratic
6log4(log8) + 3t^2 = 8log8(t)

After re-arranging, use the quadratic formula to solve for t, after that sub back into logx = t to get x

check my steps, easy to make typos here.