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Logarithms Calculator

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Example
Created on 2024-06-20Asked by Sebastian Martin (Solvelet student)
Simplify the expression log⁡2(32)+log⁡2(4)−log⁡2(16) \log_2 (32) + \log_2 (4) - \log_2 (16) .

Solution

To simplify the expression log⁡2(32)+log⁡2(4)−log⁡2(16) \log_2 (32) + \log_2 (4) - \log_2 (16) , use the properties of logarithms. First, use the fact that log⁡b(mn)=log⁡b(m)+log⁡b(n) \log_b (mn) = \log_b (m) + \log_b (n) : log⁡2(32)+log⁡2(4)=log⁡2(32⋅4) \log_2 (32) + \log_2 (4) = \log_2 (32 \cdot 4) Next, calculate the product inside the logarithm: 32⋅4=128 32 \cdot 4 = 128 So, the expression becomes: log⁡2(128)−log⁡2(16) \log_2 (128) - \log_2 (16) Use the property that log⁡b(mn)=log⁡b(m)−log⁡b(n) \log_b \left( \frac{m}{n} \right) = \log_b (m) - \log_b (n) : log⁡2(128)−log⁡2(16)=log⁡2(12816) \log_2 (128) - \log_2 (16) = \log_2 \left( \frac{128}{16} \right) Calculate the quotient inside the logarithm: 12816=8 \frac{128}{16} = 8 So, the expression simplifies to: log⁡2(8) \log_2 (8) Finally, evaluate the logarithm: log⁡2(8)=3 \log_2 (8) = 3 Therefore, the simplified expression is: log⁡2(32)+log⁡2(4)−log⁡2(16)=3 \log_2 (32) + \log_2 (4) - \log_2 (16) = 3 Solved on Solvelet with Basic AI Model
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1. Evaluate the logarithm log⁡5(125) \log_5(125) .2. Solve the equation log⁡(x+3)=2\log(x + 3) = 2 for xx.
DefinitionLogarithms are mathematical functions which quantify the power to which a base number must be raised in order to yield a give number. The logarithm of x with base b is defined as the power y the base needs to be held up to in order to get x. This idea is written as: logb​(x)=y↔by=x. Example: log10​(100)=2 because 102=100.
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