what is the value of log0.5 16 (0.5 is the small bottom number) -4.00 -0.25 1.51 2.41

Question

what is the value of log0.5 16 (0.5 is the small bottom number)
-4.00
-0.25
1.51
2.41

0

Answers ( No )

    0
    2021-10-11T05:38:59+00:00

    Answer : -4.00

    what is the value of  log_{0.5}(16)

    We use log property to find the value

    16 = 2*2*2*2 = 2^4

    So we replace 16 by 2^4

    log_{0.5}(2^4)

    As per log property we move exponent before log

    4 log_{0.5}(2)

    0.5  can be written as 1/2 . 1/2 can be written as 2^-1

    4 log_{2^-1}(2)

    Now we apply change of base formula

    log_a(b) = \frac{log a}{log b}

    4 log_{2^-1}(2)=4 \frac{log 2}{log 2^-1}

    Move the exponent -1 before log

    4 \frac{log 2}{-1log 2}

    log 2 will get cancelled

    \frac{4}{-1}

    -4

    -4.00 is the final answer

    0
    2021-10-11T05:39:57+00:00

    we are given

    log_0_._5(16)

    Firstly, we will factor out 16

    16=2\times 2\times 2\times 2\times 2

    16=2^4

    we can write it as

    16=(\frac{1}{2})^{-4}=(0.5)^{-4}

    we can replace it as

    log_0_._5(16)=log_0_._5((\frac{1}{2})^{-4})

    now, we can use property of log

    log_a(b^n)=nlog_a(b)

    we get

    log_0_._5(16)=-4log_0_._5(0.5)

    log_0_._5(16)=-4\times 1

    log_0_._5(16)=-4………….Answer

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