Prove that
logo V27 + log,, 8+ log,0 V1000
log10 120
(without using the tables).
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Step-by-step explanation:
log √27+log8-log√1000 /log1.2
= log(√27x8÷10√10) / log1.2
= log(3√3 x 4/ 5√10) /log1.2
= log12√3 - log5√10 / log1.2
= log ( 432 ÷250)^1/2/ log1.2
= log ( 216÷125)^1/2 /log1.2
= log [( 6÷ 5)^3]^1/2 /log1.2
= log(6/5)^3/2 /log1.2
= 3/2log1.2 / log1.2
= 3/2 ANS
Following Laws of logarithm to any base are applied to compute the above
(1) log(axb) = loga + logb
(2) log (a÷b) = loga - logb
(3) loga^b = b (loga )
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