Find the vale of p,p in each of the following: 1. log,base,2,32,equals ,p,LOG2 32=p. 2. base,p,81,equals,2,LOGp81=2​

Find the vale of p,p in each of the following: 1. log,base,2,32,equals ,p,LOG2 32=p. 2. base,p,81,equals,2,LOGp81=2​

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Sophia

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  1. Given : log₂32=p

    [tex]\log_p81=2[/tex]

    To Find : Value of p

    Solution:

    log₂32=p

    => log₂2⁵=p

    log aⁿ = n log a

    => 5 log₂2 =p

    logₐa= 1

    => 5 ( 1) = p

    => p = 5

    [tex]\log_p81=2[/tex]

    Dividing both sides by 2

    => [tex]\frac{1}{2} \log_p81=1[/tex]

    => [tex]\log_p81^{\frac{1}{2} }=1[/tex]

    => [tex]\log_p9=1[/tex]

    => p = 9

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