Question

Choose the correct option.
Simplify the expression 7logs p + 3/2 logs Q-1/2 logs 2r.​

Answer 1

Explanation:

i did,nt understand the question

Answer 2

The simplified expression is log base 5 ((p^7*q^3/2)/2r^1/2).

Given,

7logs p + 3/2 logs Q-1/2 logs 2r.​

To Find,

Simplify the expression,

Solution,

We can solve the question as follows:

It is asked that we have to simplify the given expression. The expression is:

$7log_{5} p + \frac{3}{2} log_{5} q - \frac{1}{2} log_{5}2r$

According to the power property of logarithms,

$n log_{b} a = log_{b} a^{n}$

Therefore, the given expression can be written as,

$= log_{5} p^{7} + log_{5} q^{\frac{3}{2}} - log_{5}2r^{\frac{1}{2}}$

Since all the logarithmic values have the same base, the positive values can be multiplied and the negative values can be divided.

$log\:x + log\:y = log\:(x*y)$ and $log\: x - log\: y = log\frac{x}{y}$

Therefore,

$= log_{5} (\frac{p^{7}*q^{\frac{3}{2} } }{2r^{\frac{1}{2} } } )$

Hence, the simplified expression is log base 5 ((p^7*q^3/2)/2r^1/2).

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