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 What is log 4 16

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How to use the log function 

 May 12, 2015

Best Answer 

 #1
avatar+413 
+8
Once you understand what a logarithm is, these problems become pretty easy. Logarithms are exponents. The specific logarithm,  log%284%2C+%2816%29%29, is the exponent for 4 that results in 16. So we ask ourselves, what power of 4 is 16? Or 4 to what power is 16? The answer: 2! So:
log%284%2C+%2816%29%29+=+2

log%284%2C+%281%2F16%29%29
 

What power of 4 is 1/16? If you understand negative exponents then you will understand that if  4%5E2+=+16 then  4%5E%28-2%29+=+1%2F16. So:
log%284%2C+%281%2F16%29%29+=+-2

log%284%2C+%281%2F256%29%29
I will leave this one up to you. Hint:  4%5E4+=+256.
 May 12, 2015

2+0 Answers

 #1
avatar+413 
+8
Best Answer
Once you understand what a logarithm is, these problems become pretty easy. Logarithms are exponents. The specific logarithm,  log%284%2C+%2816%29%29, is the exponent for 4 that results in 16. So we ask ourselves, what power of 4 is 16? Or 4 to what power is 16? The answer: 2! So:
log%284%2C+%2816%29%29+=+2

log%284%2C+%281%2F16%29%29
 

What power of 4 is 1/16? If you understand negative exponents then you will understand that if  4%5E2+=+16 then  4%5E%28-2%29+=+1%2F16. So:
log%284%2C+%281%2F16%29%29+=+-2

log%284%2C+%281%2F256%29%29
I will leave this one up to you. Hint:  4%5E4+=+256.
kes1968 May 12, 2015
 #2
avatar+33661 
+5

If you use the calculator on this site, you can type in log(16,4) to get the log to base 4 of 16.  More generally, to get log to base b of x type in log(x,b)

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 May 12, 2015

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