Please solve this

Asked by aastharoy997 | 30th Mar, 2020, 01:09: PM

Expert Answer:

To find the value of log58+2log525-3log5320+3log532
log subscript 5 8 space plus space 2 log subscript 5 25 space minus space 3 log subscript 5 320 space plus space 3 log subscript 5 32
equals log subscript 5 space 8 space plus space 2 log subscript 5 space 5 squared space minus space 3 log subscript 5 space open parentheses 5 cross times 64 close parentheses space plus space log subscript 5 space 32 cubed space... space left parenthesis S i n c e space a log space x equals log space x to the power of a right parenthesis
equals log subscript 5 space 2 cubed space plus space 4 log subscript 5 space 5 space minus space 3 log subscript 5 space 5 space minus space 3 log subscript 5 space 64 space plus space log subscript 5 space 32 cubed space space left parenthesis S i n c e space log space a space plus space log space b space equals space log space a b right parenthesis
equals log subscript 5 space 2 cubed space plus space 4 space minus space 3 space minus log subscript 5 space 64 cubed space plus space log subscript 5 space 32 cubed space space.... space left parenthesis S i n c e space log subscript a a equals 1 right parenthesis
equals 1 plus space log subscript 5 space 2 cubed space plus space log subscript 5 space 32 cubed space minus log subscript 5 space 64 cubed
equals 1 space plus space log subscript 5 open parentheses 2 cubed cross times 32 cubed close parentheses minus log subscript 5 64 cubed space... space left parenthesis S i n c e space log space a space plus space log space b space equals space log space a b right parenthesis
equals 1 space plus space log subscript 5 open parentheses fraction numerator 2 cubed cross times 32 cubed over denominator 64 cubed end fraction close parentheses space... space open parentheses S i n c e space log space a space minus space log space b space equals space log a over b close parentheses
equals 1 plus log subscript 5 open parentheses fraction numerator 2 cubed cross times 2 to the power of 15 over denominator open parentheses 2 to the power of 6 close parentheses cubed end fraction close parentheses
equals 1 plus log subscript 5 1
equals 1
H e n c e comma space log subscript 5 8 space plus space 2 log subscript 5 25 space minus space 3 log subscript 5 320 space plus space 3 log subscript 5 32 equals 1

Answered by Renu Varma | 30th Mar, 2020, 06:35: PM

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