Question

Write the expression 4 log x − 6 log (x + 2) as a single logarithm

Answer 1

To write the expression 4 log x − 6 log (x + 2) as a single logarithm, apply the properties of logarithms.

Step-by-step explanation:

To write the expression 4 log x − 6 log (x + 2) as a single logarithm, we can make use of the following logarithmic properties:

1. The logarithm of a product of two numbers is the sum of the logarithms of the two numbers: log(xy) = log(x) + log(y)
2. The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number: log(x^n) = n log(x)
3. The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers: log(x/y) = log(x) - log(y)

Using these properties, we can simplify the given expression as follows:

4 log x − 6 log (x + 2) = log(x^4) - log((x + 2)^6)

Therefore, the expression can be written as the single logarithm log(x^4) - log((x + 2)^6).

Answer 2

the first step in condensing this expression is change your coefficients into exponents (power property).

4 log x − 6 log (x + 2)
log x⁴ - log (x + 2)⁶

now you can use log properties to combine this into a single logarithm. once you change the coefficients, you can now see that this is simply a log minus another log--and that subtraction symbol actually becomes division by the logarithm quotient property.

log (x⁴)/(x + 2)⁶ is the condensed version of this logarithm. in case the formatting isn't easy to read, it's log of x to the fourth power over x plus 2 to the sixth power.