Question

Write the following expression as a single logarithm with coefficient 1. log 9 10- log9 1/2-log9 4

Answer 1

we are given

$log_9(10)-log_9(\frac{1}{2} )-log_9(4)$

we can also write as

$log_9(10)-(log_9(\frac{1}{2} )+log_9(4))$

Since, the base of logs are same

so, we can use property

$log_a(b)+log_a(c)=log_a(b\times c)$

$log_9(10)-(log_9(\frac{1}{2}\times 4)$

$log_9(10)-log_9(2)$

we can use property of log

$log_a(b)-log_a(c)=log_a(\frac{b}{c} )$

so, we get

$log_9(10)-log_9(2)=log_9(\frac{10}{2} )$

$log_9(10)-log_9(2)=log_9(5)$

So, we get

$log_9(10)-log_9(\frac{1}{2} )-log_9(4)=log_9(5)$.............Answer

Answer 2

The equivalent logarithmic expression is $\log_9(5)$

The logarithm expression is given as:

$\log_9(10) - \log_9(1/2) - \log_9(4)$

Apply the quotient rule of logarithm on the above expression

$\log_9(10) - \log_9(1/2) - \log_9(4) = \log_9(10 \div 1/2 \div 4)$

Divide 10 by 1/2

$\log_9(10) - \log_9(1/2) - \log_9(4) = \log_9(20 \div 4)$

Divide 20 by 4

$\log_9(10) - \log_9(1/2) - \log_9(4) = \log_9(5)$

Hence, the equivalent logarithmic expression is $\log_9(5)$

Read more about logarithmic expressions at:

https://brainly.com/question/10727370