This can be rewritten as log 2 (32)1/2 = z Let us convert it to exponential form (3/2)z = (27/8) This equation is not as difficult as it may seem. We know that 121 is 11 squared, and hence the square root of 121 is 11. To find z, first let us convert this to exponential form: 121z = 11 Here 64 needs to be converted to (1/4) raised to an exponent, which is the solution to the logarithm. Now let us try to find z, by simplifying the equation This can be written in another form as: 4z = 1/64 Let us consider that log 4 (1/64) equals to z Some logarithms are more complicated but can still be solved without a calculator. In such cases, it is understood that the base value by default is 10. It is to be noted that in some instances you might notice that the base is not mentioned. One the base and the number in the parenthesis are identical, the exponent of the number is the solution to the logarithm. Let us try to replace the number in the parenthesis with the base raised to an exponent. Let us use an example to understand this further: log 5 (25) Remembering and understanding this equivalency is the key to solving logarithmic problems. Here log x (y) is known as the logarithmic form, and xz = y is known as the exponential form. In other words, x needs to be raised to the power z to produce y. If xz = y, then ‘z’ is the answer to the log of y with base x, i.e., log x (y) = z The solution of any logarithm is the power or exponent to which the base must be raised to reach the number mentioned in the parenthesis. We first need to understand square, cubes, and roots of a number. Now, let’s get to the main part: How to Solve a Log Without Using a Calculator? The number that needs to be raised is called the base. Defining a logarithm or logĪ logarithm is defined as the power or exponent to which a number must be raised to derive a certain number. To solve a logarithm without a calculator, let us first understand what a logarithm is. Logarithms are an integral part of the calculus.
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