Write the following expressions as log N and find their values.

(i) log2 + log5

(ii) log₂16 – log₂2

(iii) 3 log₆₄ 4

(iv) 2 log3 – 3 log 2

(v) log 10 + 2 log 3 – log 2

I. log2 + log5

using the property of logarithmic, log_a xy = log_ax + log_ay

= log(2×5)

= log10

II. log₂16 – log₂2

using the property of logarithmic, and

=

= log₂ 8 = log₂2³

= 3log₂ 2 [∵]

= 3 [ log₂ 2 = 1]

III. 3 log₆₄ 4

Using the property of logarithmic,

= log₆₄4³ 

= log₆₄ 64

=

IV. 2 log3 - 3 log2

using the property of logarithmic, and

= log3²-log2³

=

=

V. log 10 + 2 log3 - log2

using the property of logarithmic, log_a xy = log_ax + log_ay

= log5 + log2 + log3²-log2

= log5 + log9

= log(5×9)

= log45