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Write 3log7x-4log7y as a single logarithm.

Sagot :

ophysto

Answer:

[tex]3\log7x - 4\log7y = log(\frac{x^3}{7y^4} )[/tex]

Step-by-step explanation:

The given logarithm can be re-written as:

[tex]\log(7x)^3 - log(7y)^4[/tex]

For the power property:

[tex]\log_ba^c = c\log_ba[/tex]

Know for the quotient property you get:

[tex]log_ba - log_bc = log(\frac{a}{c} )[/tex]

[tex]\log{\frac{(7x)^3}{(7y)^4} } =\log{\frac{7^3x^3}{7^4y^4} } =\log{\frac{x^3}{7y^4} }[/tex]

so the final answer is [tex]\log{\frac{x^3}{7y^4} }[/tex]

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