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

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Mathematics

Hailee Schwartz

3 June, 19:48

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

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Azul Rangel · Answer 1

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

4 log x - 6 log (x + 2)

log x ⁴ - 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.