Problem

Use the properties of logarithms to rewrite the following expression as a sum or difference of logarithms each of which is the logarithm of an integer or a variable. Assume all variables represent positive real numbers.
log10(7x2)
log10(7x2)=

Answer

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Answer

This is the simplest form of the expression, and it meets the requirements of the problem.

Steps

Step 1 :Rewrite the given expression using the property of logarithms logb(mn)=logb(m)+logb(n): log10(7x2)=log10(7x)log10(2)

Step 2 :Use the property of logarithms again to separate the 7 and x in the first term: log10(7x)=log10(7)+log10(x)

Step 3 :Substitute this back into the original expression: log10(7x2)=log10(7)+log10(x)log10(2)

Step 4 :This is the simplest form of the expression, and it meets the requirements of the problem.

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