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Free Logarithms Calculator - Simplify logarithmic expressions using algebraic rules step-by-step.
The below is the work with steps to find what is log base 2 of 8 shows how the input values are being used in the log base 2 functions. Formula: log b (x) = y, if b y = x. Input: x = 8. b = 2. Solution: y = log 2 8.
Enter the logarithmic expression below which you want to simplify. The logarithm calculator simplifies the given logarithmic expression by using the laws of logarithms.
log b (x × y) = log b x + log b y. EX: log (1 × 10) = log (1) + log (10) = 0 + 1 = 1. When the argument of a logarithm is a fraction, the logarithm can be re-written as the subtraction of the logarithm of the numerator minus the logarithm of the denominator. log b (x / y) = log b x - log b y.
In other words, the logarithm of x to base b is the unique real number y such that displaystylebʸ=x. The logarithm is denoted "logb x". An equivalent and more succinct definition is that the function logb is the inverse function to the function displaystylexmapstobˣ. log₂ 16 = 4, since 2⁴ = 2 × 2 × 2 × 2 = 16.
The logarithmic function, y = log b (x) is the inverse function of the exponential function, x = by. So if we calculate the exponential function of the logarithm of x (x>0), f (f -1 (x)) = blogb(x) = x. Or if we calculate the logarithm of the exponential function of x, f -1 (f (x)) = log b (bx) = x.
Rewrite as an equation. log2(8) = x log 2 (8) = x. Rewrite log2 (8) = x log 2 (8) = x in exponential form using the definition of a logarithm. If x x and b b are positive real numbers and b b does not equal 1 1, then logb (x) = y log b (x) = y is equivalent to by = x b y = x. 2x = 8 2 x = 8.
