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ICSE Class 9 Answered

  If a power 3-x multiplied with b power 5x which is equal to a power x+5 multiplied with b power 3x, then x log b/a is.
Asked by pravallika.kaki | 15 Feb, 2018, 07:25: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight a to the power of 3 minus straight x end exponent straight b to the power of 5 straight x end exponent equals straight a to the power of straight x plus 5 end exponent straight b to the power of 3 straight x end exponent
straight a to the power of 3 minus straight x end exponent over straight a to the power of straight x plus 5 end exponent equals straight b to the power of 3 straight x end exponent over straight b to the power of 5 straight x end exponent
straight a to the power of 3 minus straight x minus straight x minus 5 end exponent equals straight b to the power of 3 straight x minus 5 straight x end exponent
straight a to the power of negative 2 minus 2 straight x end exponent equals straight b to the power of negative 2 straight x end exponent
Taking space log space on space both space sides
log space straight a to the power of negative 2 minus 2 straight x end exponent equals log space straight b to the power of negative 2 straight x end exponent
left parenthesis negative 2 minus 2 straight x right parenthesis loga equals negative 2 xlogb
minus 2 left parenthesis straight x plus 1 right parenthesis loga equals negative 2 xlogb
xlogb over loga equals straight x plus 1
end style
Answered by Sneha shidid | 16 Feb, 2018, 10:00: AM
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