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galina1969 [7]
3 years ago
6

What is the value of log0.5 16 (0.5 is the small bottom number)-4.00-0.251.512.41

Mathematics
2 answers:
MArishka [77]3 years ago
8 0

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


eduard3 years ago
4 0

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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