Help Please!

a = (8 log(30))/(log(5)), b = (8 log(30))/(log(3)), c = (8 log(30))/(log(2)), x = 656,100,000,000

Don't really understand this one!! CPhill to the rescue!.

log 5 = a     log 3 = b   log 2 = c    find log₃₀ 8

Note :  log 5 + log 3 + log 2   = a + b + c     and we can write

log (5 * 3) + log 2  = a + b + c

log15 + log 2  = a + b + c

log (15 * 2)  = a + b + c

log (30) = a + b + c 

And note, using the change of base rule ...  log₃₀ 8  =  log8 / log 30 ......so....

log₃₀ 8  =  log8 / log 30  = log 8 / [ a + b + c ] =    log 8 / [ log 5 + log 3 + log 2]  ≈ .611