Express as a sum, difference, and product of logarithms, without using exponents log18 7�ãx/y
To express log18 7�ãx/y as a sum, difference, and product of logarithms, we can use several logarithmic properties.
1. Sum Property:
log_a (b * c) = log_a (b) + log_a (c)
2. Difference Property:
log_a (b / c) = log_a (b) - log_a (c)
3. Product Property:
log_a (b^c) = c * log_a (b)
Using these properties, we can rewrite log18 7�ãx/y as follows:
log18 7�ãx/y = log18 7 + log18 (�ãx/y)
Therefore, log18 7�ãx/y can be expressed as the sum of log18 7 and log18 (�ãx/y).
To express log18 (7x/y) as a sum, difference, and product of logarithms, we can use the properties of logarithms.
1. Sum of logarithms:
The sum of logarithms states that log base b (a) + log base b (c) = log base b (a * c).
So, we can rewrite log18 (7x/y) using the sum of logarithms as:
log18 (7x / y) = log18 (7x) - log18 (y)
2. Difference of logarithms:
The difference of logarithms states that log base b (a) - log base b (c) = log base b (a / c).
So, we can rewrite the expression using the difference of logarithms as:
log18 (7x / y) = log18 (7x) - log18 (y)
3. Product of logarithms:
The product of logarithms states that log base b (a) * log base b (c) = log base b (a^c).
To use the product of logarithms, we need to convert the division in the expression to a multiplication. This can be done by multiplying by the reciprocal of y.
So, we can rewrite the expression using the product of logarithms as:
log18 (7x / y) = log18 (7x * (1/y))
Keep in mind that while all these expressions represent the same value, they may be more suitable for different calculations or simplifications depending on the context.