Question

If log3of2=0.6309 and lo3of5=1.465, evaluate without the use of calculators. (a)log3of10, (b)log3of15, (c)log3of2.5

Answer 1

Answer:  2.0959       2.465            0.8341

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Step-by-step explanation:

log ₃2=0.6309

log ₃5=1.465

Now,

i )log ₃10 = log ₃ ( 2*5 ) = log ₃2 + log ₃ 5 =  0.6309  + 1.465 = 2.0959

ii) log₃ (15) = log₃ ( 3*5) = log₃ 3 + log ₃5 = 1 +  1.465 = 2.465

iii) log₃ (2.5) = log ₃ ( 25/10 ) = log ₃25 - log ₃10

                                        = log ₃ ( 5^2 ) -  2.0959

                                       = 2 log ₃ 5 -2.0959

                                      = 2 * 1.465 - 2.0959

                                     = 2.93 -2.0959

                                     = 0.8341