Question

Write the expression as a sum and or a difference of logarithms, with all variables to the first degree

Answer 1

The logarithm expanding expression is log 5 + 8 log x + 3 log y.

What is expanding of logarithm expression?

  Using the power rule if necessary, write logarithms as a sum or difference of logarithms to extend them. It is frequently beneficial to employ the quotient rule, product rule, and power rule in that order. Write logarithms as one logarithm to make them easier to understand.

Here the given expression is ,

=> ㏒ 5$x^8 y^3$

Now using logarithm rule,

=> log(a*b*c) = log a+ log b +log c

Then,

=> log 5$x^8 y^3$ = log 5 + log$x^8$ + log$y^3$

Now we know that log$a^b$ = b log a. then,

=> log 5$x^8 y^3$ = log 5 + 8 log x + 3 log y.

Therefore the expression is log 5 + 8 log x + 3 log y.

To learn more about logarithm expressions

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