Question

Arjun incorrectly writes log7 + log7 − log7 as a single logarithm. log7+1og7 y-log7 z =log7 (x+y-z) Where did Arjun make errors? Explain his errors and the properties of logarithms that leads to the correct answer. State the correct answer.

Answer 1

Arjun should have used the property that the logarithm of a product is the sum of the logarithms and that the logarithm of a division is the difference of the logarithms to combine the expressions correctly.

Step-by-step explanation:

Corrections to Logarithmic Expression

Arjun made errors when trying to combine the logarithmic expressions log7 x, log7 y, and -log7 z into a single logarithm. The correct property to use here is that the logarithm of the product of two numbers is the sum of the logarithms of the two numbers: log xy = log x + log y. Conversely, the logarithm of the division of two numbers is the difference between the logarithms of the two separate numbers: log (x/y) = log x - log y.

Therefore, the correct expression for combining Arjun's logarithms should be:

log7(xy/z) = log7 x + log7 y - log7 z.

This takes advantage of both the multiplication and division properties of logarithms.