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log316 - log32 = log38

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Q: Which logarithm is equivalent to log base 3 16 - log base 3 2?
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How do you solve log base16 8?

You divide log 8 / log 16. Calculate the logarithm in any base, but use the same base for both - for example, ln 8 / ln 16.


A logarithm is an exponent?

A logarithm is quite the opposite of an exponential function. Whereas an exponential is y=ax , a log is logay=x For example, log39=2 because you raise 3 by the 2nd power to get 9. In other words, log39=2 because 32=9 Logarithms are present because they are a handy way to solve exponential equations, and because calculators use them to great advantage.


What is log base 4 of 16?

The answer is 16


What is logarithm in simple terms?

The power to which a 'base number' (usually 10) has to be raised to produce a given number. as an example: Log (base 10) of 100 = 2 ............ because 10 raised to the power of 2 (or 10 squared) or 10 x 10 = 100 log (base 10) of 1000 = 3 ........... because 10 raised to the power of 3 (or 10 cubed) or 10 x 10 x10 = 1000 log (base 10) of 1000000000 = 9 ... because 10 raised to the powr of 9 or 10x10x10x10x10x10x10x10x10 = 1000000000 In a similar way log (base 2) of 16 = 4................. because 2x2x2x2 (2 raised to the power of 4) = 16 and so on.


How do you solve 16 as a power of 2?

In this case, trial and error is probably the easiest: 22 = 4, 23 = 8, 24 = 16 yes! A more genral answer is: the power that you want is log(16)/log(2) where the logarithm is calculated to any base (10 or e , or indeed any other).


Evaluate 81 to the power of log 16 with a base of 9?

It is 256.


What is the logarithm of 16 to the base 4?

There are two ways to solve this. One is using the definition of logarithms: solve the equation 4x = 16. This can be done by inspection, in this case. The other is to use a change-of-base, to change to a base your calculator can handle. For example, changing to base e: log416 = ln(16) / ln(4)


How do you solve the equation 5.2 log4 2x16?

Due to limitations with browsers mathematical operators (especially + =) get stripped from questions (leaving questions with not enough information to answer them) and it is not entirely clear what the log4 bit means. I guess that the log4 bit is logarithms to base 4 of 2x^16 (which I'll write as log_4(2x^16) for brevity). If this is so, use normal algebraic operations to make log_4(2x^16) the subject of the equation. With logs there are useful rules; given 2 numbers 'a' and 'b': log(ab) = log(a) + log(b) log(a^b) = b × log(a) Which means: log_4(2x^16) = log_4(2) + log_4(x^16) = log_4(2) + 16 × log(x) and the equation can be further rearranged: log_4(2x^16) = <whatever> → log_4(2) + 16 × log(x) = <whatever> → log(x) = (<whatever> - log_4(2)) / 16 Logarithms tell you the power to which the base of the logarithm must be raised to get its argument, for example when using common logs: lg 100 = 2 since 10 must be raised to the power 2 to get 100, ie 10² = 100. (lg is the abbreviation for logs to base 10; ln, or natural logs, is the abbreviation for logs to the base e.) With logs to base 4, it is 4 that is raised to the power of the log to get the original value. eg log_4(16) = 2 since 4^2 = 16. log_4(2) can be worked out: The log to any base of the base is 1 (since any number to the power 1 is itself). Now 2 × 2 = 2² = 4. → log_4(4) = 1 → log_4(2²) = 1 → 2 × log_4(2) = 1 → log_4(2) = ½ → log(x) = (<whatever> - ½) / 16 Back to the rearranged equation; with logs to base 4, if you make both sides the power of 4 you'll get: 4^(log_4(x)) = 4^(<whatever>) → x = 4^(<whatever>) which now solves for x.


How do you write a number as a power of 2?

For an exact power of 2 (1, 2, 4, 8, 16, 32, etc., but also 1/2, 1/4, etc.), you can try out different exponents until you get it right. To write any number (greater than 0) as a power of 2 is equivalent to taking the logarithm of that number in base 2, which is the same (if you call your number "n") as calculating log n / log 2 (using the same base for both logarithms - for example, both in base 10, or both in base e).


What is a logarithm?

Logarithms are the INVERSE function of powers/exponentials. a = b^(c) Then its inverse is log(b) a = c As a number set / 10^3 = 1000 Then log(10)1000 = 3


What is the hexadecimal equivalent of the decimal number 1016?

1016 in base 10 = 3F8 in base 16.


What is 9 to the power of 16?

The answer sought can be approximated by using logarithms. The logarithm of 916 = 16 X log (9) = 15.26788015. The integral part of this number is the power of 10 in the answer, and the other part of the answer is the antilog of 0.26788015 or 1.853020184. Therefore, 1.853020184 x 1015 is the answer, to the largest number of digits on my calculator, assuming that the 9 and 16 are taken as exact.