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We write it like this: log2(8) = 3. So these two things are the same: The number we multiply is called the "base", so we can say: "the logarithm of 8 with base 2 is 3". or "log base 2 of 8 is 3". or "the base-2 log of 8 is 3".
The three laws of logarithms. W HEN WE ARE GIVEN the base 2, for example, and exponent 3, then we can evaluate 2 3. 2 3 = 8. Inversely, if we are given the base 2 and its power 8 -- 2? = 8. -- then what is the exponent that will produce 8? That exponent is called a logarithm. We call the exponent 3 the logarithm of 8 with base 2. We write.
Algebra. Evaluate log base 2 of 8. log2 (8) log 2 (8) 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.
log 2 (x) + log 2 (x-3) = 2. Solution: Using the product rule: log 2 (x∙(x-3)) = 2. Changing the logarithm form according to the logarithm definition: x∙(x-3) = 2 2. Or. x 2-3x-4 = 0. Solving the quadratic equation: x 1,2 = [3±√(9+16) ] / 2 = [3±5] / 2 = 4,-1. Since the logarithm is not defined for negative numbers, the answer is: x = 4 ...
The graph of the logarithm base 2 crosses the x-axis at x = 1 and passes through the points (2, 1), (4, 2), and (8, 3), depicting, e.g., log 2 (8) = 3 and 2 3 = 8. The graph gets arbitrarily close to the y-axis, but does not meet it. Addition, multiplication, and exponentiation are three of the most fundamental arithmetic operations.
One step at a time: log means "exponent" or "power". ----------------. 2log2 8 means "twice the exponent of 2 that gives you the number 8. ----------------. So what exponent of 2 gives you the number 8? 2^3 = 8. So log2 8 is 3. Twice that is 6.
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.
