SOLUTION: use the properties of logarithms to elimate products, quotients and exponents from the following expression: log3[9 sqrt(x-5)/(x-1)^(5)] Thank you

Question 387318: use the properties of logarithms to elimate products, quotients and exponents from the following expression: log3[9 sqrt(x-5)/(x-1)^(5)]
Thank you
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

First we can use the property for quotients, , to split the single logarithm into the difference of the logarithms of the numerator and denominator:

On the first logarithm we can use the property for products to split the logarithm of the product into the sum of the logarithms of its factors:

Since square roots are the same as an exponent of 1/2 we can rewrite the second logarithm as a power of x-5:

Now we can use the property for exponents to rewrite the last two logarithms:

Last of all the first logarithm is one we can find (without a calculator). Since then the first logarithm must be 2:

This is as far as we can go.
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