Answer :
To solve this problem you must apply the proccedure shown below:
1. You have the following expresssion given in the problem above:
[tex]log(s)log(r)+8log(rs)-3log(rt) [/tex]
2. By using the logarithms properties, you have that the product of two logarithms can be written as a sum:
[tex]log(s+r)+8log(rs)-3log(rt) [/tex]
3. The sum can written as a product and the susbtraction as a division. The number 8 and 3 can be written as exponents:
[tex]log(s+r)(rs)^8/(rt)^3 [/tex]
Therefore, the answer is: [tex]log(s+r)(rs)^8/(rt)^3[/tex]
1. You have the following expresssion given in the problem above:
[tex]log(s)log(r)+8log(rs)-3log(rt) [/tex]
2. By using the logarithms properties, you have that the product of two logarithms can be written as a sum:
[tex]log(s+r)+8log(rs)-3log(rt) [/tex]
3. The sum can written as a product and the susbtraction as a division. The number 8 and 3 can be written as exponents:
[tex]log(s+r)(rs)^8/(rt)^3 [/tex]
Therefore, the answer is: [tex]log(s+r)(rs)^8/(rt)^3[/tex]
The equivalent expression of the given logarithmic equation is [tex]\log(s+ r) + \log(rs)^8 - \log(rt)^3[/tex]
The logarithmic expression is given as:
[tex]\log(s)\log(r) + 8\log(rs) - 3\log(rt)[/tex]
Apply the product rule of logarithm
[tex]\log(s)\log(r) + 8\log(rs) - 3\log(rt) = \log(s+ r) + 8\log(rs) - 3\log(rt)[/tex]
Apply the power rule of logarithm
[tex]\log(s)\log(r) + 8\log(rs) - 3\log(rt) = \log(s+ r) + \log(rs)^8 - \log(rt)^3[/tex]
So, the equivalent expression of the given logarithmic equation is [tex]\log(s+ r) + \log(rs)^8 - \log(rt)^3[/tex]
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