Log Base 2

Log base 2 is useful to write the exponential form with a base of 2 into logarithmic form. The number 2⁰ = 1, 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, but if we have 2^x = 25 and we need to find the value of x, then we can first write it as log base 2 or \(log_225 = x\), and find the value of x. The log base 2 helps to find the exponential value of 2.

Let us learn more about log to the base of 2, conversion to exponential form, and properties of log base 2, with the help of examples, FAQs.

Log base 2 is a mathematical form of expressing any natural number as an exponential form to the base of 2. The exponential form of 2⁴ = 16 can be easily represented as a log base 2 and written as \(log_2 16 = 4\). Log N to the base of 2 is equal to expressing the number N in exponential form having a base of 2. Further, if we have to find the value of k, which is presented in the expression 2^k = 24. This is difficult but can be approximately guessed. Here log base 2 is helpful to find the value of k, and here we have \(log_2 24 = k\).

Every positive natural number can be represented as the exponent of the number 2. Here in the below table, the logarithmic form of log base 2 is represented as an exponential form to the base of 2.

Log base 2 can be converted into an exponential form with 2 as the base. Let us understand this with a simple formula. For a natural number N its log to the base of 2 is equal to k and is written as \(log_2N = k\), which can be written in exponential form as 2^k = N.

Let us look at an example of converting an exponential form to log base 2. An exponential number 8^k = 2492, need to be first written to the base of 2, as (2³)^k = 2492, or 2^3k = 2492. This can be written in log to base of 2 as \(log_22492 = 3k\). Thus we can aim at writing each of the exponential form into exponent to the base of 2, and convert the same to the logarithmic form of log base 2.

The properties of log base 2 is similar to the logarithmic properties.

• The log of 1 to the base of 2 is always equal to 0. \(log_21 = 0\).
• The log 2 to the same base of 2 is equal to 1.\(log_22 = 1\)
• The sum of log base 2 to a and log base 2 to b can be combined and written as a single log with a product ab. \(log_2a + log_2b = log_2ab\).
• The difference of log base 2 to a and the log base 2 to b can be combined and written as a single log with the division a/b. \(log_2a - log_2b = log_2 a/b\)
• The log base 2 for a number N can be written as two different logs as log N and log 2. \(log_2N = LogN/Log2\).
• The log base 2 written with a number in the exponential form can be written as the product of the exponent and the log base 2. \(log_2n^k = klog_2n\).

☛Related Topics

• Logarithms
• Properties of Logarithms
• Logarithmic Functions
• Logarithmic Differentiation

What Is Log Base 2 In Algebra?

The log base 2 to a number N in algebra is equal to the exponent value of 2 which gives the number N. The log base 2 is written in the logarithmic form as \(log_2N = k\), and the same is written in exponential form as 2^k = N.

How Do You Solve Log Base 2?

The log base 2 can be solved by transforming it into an exponential form. The log base 2 to a number N is equal to the exponent value, to which the base 2 has to be raised, to obtain the number N.

What Is The Formula For Log Base 2?

The log base 2 can be written as \(log_2N=k\), which can be further written in exponential form as 2^k = N.

What Does Log Base 2 Mean?

The log base 2 means that the power value to which the base number 2 has to be raised, to obtain the number for which log base 2 is being calculated.

What Is the Derivative of Log Base 2 To x?

The derivative of log base 2 to x is equal to 1/x.log2. This can be represented as a formula as follows.

d/dx.log₂x= d/dx.logx/log2 = 1/x . 1/log2 = 1/xlog2