Question

log10+2log3-log 2 write expansion as log N​

Answer 1

Log10 + log3² - log2,

log10 + log9 - log2,

log(10×9) - log2,

log90 - log2,

log90/2,

log45

Answer 2

Step-by-step explanation:

Logarithms laws:-

$log_{m}(a) + log_{m}(b) = log_{m}(ab) \\ log_{m}(a) - log_{m}(b) = log_{m}( \frac{a}{b} ) \\ x log_{m}(a) = log_{m}( {a}^{x} )$

Applying logarithm laws in the given question:-

= log 10 + 2 log 3 - log 2

= log 10 + log 3^2 - log 2

= log 10 + log 9 - log 2

= log 10 + log (9/2)

= log (10×9)/2

= log 90/2

= log 45

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