log(a + b) ≠ log(a) + log(b)lionely said:Without using tables:
1. Evaluate 2log102 + log10(1/2 + 1/3) + 1/3log27
2log2 + log 1 - log2 + log1 - log3 + log3 = log2..
This was my attempt but it's wrong . I think I went wrong somewhere here log10(1/2 + 1/3) but I can't find the error.
A logarithm is a mathematical function that represents the number of times a base number needs to be multiplied by itself to reach a certain value. It is the inverse function of exponentiation and is often used to solve equations involving exponential growth or decay.
To solve a logarithm, you can use the properties of logarithms, such as the product, quotient, and power rules. In this particular problem, we can use the product rule to combine the two logarithms with the same base and the power rule to bring the exponent down in front of the logarithm.
The base of a logarithm is the number that is raised to a certain power. In this problem, the base of the logarithms is 10, as indicated by the subscript 10. This means that we are using a base 10 logarithm to solve the equations.
The number in front of the logarithm, also known as the coefficient, represents the power to which the base is raised. In this problem, the number 2 in front of log10 represents 10 being raised to the power of 2, which is equal to 100.
The fraction in the logarithm equation represents the quotient rule of logarithms. This rule states that when dividing two numbers with the same base, the logarithm of the quotient is equal to the difference of the logarithms of the individual numbers. In this problem, the fraction 1/2 + 1/3 represents the quotient of (1/2)/(1/3), which simplifies to 3/2.