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If Log102 = a and Log103 = B ; Express Each of the Following in Terms of 'A' and 'B': Log 2.25 - Mathematics

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प्रश्न

If log102 = a and log103 = b ; express each of the following in terms of 'a' and 'b': log 2.25

योग
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उत्तर

log102 = a and log103 = b
log 2.25

= log`225/100`

= log`[25 xx 9 ]/[ 25 xx 4 ]`

= log`[25 xx 9 ]/[ 25 xx 4 ]`

= log`(9/4)`

= `log (3/2)^2`

= `log (3/2)`                 ...[ nlogam = logamn ]

= 2( log3 - log2 )        ...[ logam - logan = loga`(m/n)`]
= 2( b - a )                  ...[ ∵ log102 = a and log103 = b ]
= 2b - 2a

shaalaa.com
Expansion of Expressions with the Help of Laws of Logarithm
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 8: Logarithms - Exercise 8 (B) [पृष्ठ १०७]

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सेलिना Concise Mathematics [English] Class 9 ICSE
अध्याय 8 Logarithms
Exercise 8 (B) | Q 11.2 | पृष्ठ १०७
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