急 ! Logarithmic Function 1

here would not give you the exact answer but combine to a other simple log function only.

a. (base 10)
2 + 3 log 8
= log 100 + log (8^3)
= log 100 + log 512
= log (100 x 512)
= log 51200

b. (base 10)
log 5 - 2 log 7
= log 5 - log (7^2)
= log 5 - log 49
= log (5/49)

c. (base 10)
log 4 / log 9
= log (2^2) / log (3^2)
= [2log 2] / [2log 3]
= log 2 / log 3

d. (base 10)
log 3^2 x log 6
= (2log 3) [log (3x2)]
= (2log 3) [log 3 + log 2]

e.
5 log10 12 + log3 20 - log10 9^3
= log10 (12^5) + [log10 20/log10 3] - log10 (9^3)
= log10 [(12^5)/(9^3))] + [log10 20/log10 3]
= log10 [(3^5)x(4^5)x20/(3^6))] + [1/log10 3]
= log10 [(4^6)x5/3)] + [1/log10 3]
= log10 [20480/3] + [1/log10 3]

f.
log4 0.3 + log1/2 18
= [log10 0.3/log10 4] + [log10 (1/2)/log10 18]
= [log10 0.3/2 log10 2] - [log10 2/2 log10 3]
= [(log10 3) - (log10 10)]/2 log10 2 - [log10 2/2 log10 3]
= [(log10 3) - 1]/2 log10 2 - [log10 2/2 log10 3]