LOGARITHMS 18

If Log_b343 – log 0.001 = 8; find b

Solution

Log_b343 – log 0.001 = 6;            [0.001=10^-3 ]

Log_b343 – log 10^-3 = 6      

Log_b343 – (-3log 10) = 6

Log_b343 + 3log 10 = 6   [remember log 10 = 1]

Log_b343 + (3 x 1) = 6

Log_b343 + 3 = 6

Log_b343 = 6 - 3

Log_b343 = 3     [Change it into exponential notation]

343 = b³

7³ = b³      [ 243 = 7³ by prime factorization]

7³ = b³  [ bases are same on both sides, so they cancel out ]

b = 7

Hence b = 7    

TRY THIS..............

If Log_a64 – log 0.00001 = 11; find a