Question

Evaluate:
$\log_{10} 2 + 16\log_{10} \big(\frac{16}{15} \big) +12 \log_{10} \big(\frac{25}{24} \big) + 7\log_{10} \big(\frac{81}{80} \big)$

Answer 1

Please see the attachment

Answer 2

Answer:

Value = 1

Step-by-step explanation:

As per the question,

We have given logarithmic equation,

$log_{10}\ 2 + 16log_{10}\ (\frac{16}{15})+12log_{10}\ (\frac{25}{24})+7log_{10}\ (\frac{81}{80})$

AS we know  the property of logarithm:

$log_{y} \ x^{n} = n\cdot log_{y}\ x$

$log_y}\ x=\frac{log\ x}{log\ y}$

$log\ 10 = 1$

$log_10\ {10} =1$

Now using this property in given equation, we get

$log_{10}\ 2 + 16log_{10}\ (\frac{16}{15})+12log_{10}\ (\frac{25}{24})+7log_{10}\ (\frac{81}{80})$

$\frac{log\ 2}{log\ 10}+16\cdot \frac{log\ (\frac{16}{15})}{log\ 10}+12\cdot \frac{log\ (\frac{25}{24})}{log\ 10}+7\cdot \frac{log\ (\frac{81}{80})}{log\ 10}$

On further soving, we get

$log_{10}\ 10$

= 1

Hence, the required answer = 1