Question

Plz solve this, logarithm question.... ​

Answer 1

Answer:

the required solution is in the above pics

Answer 2

1

Step-by-step explanation:

Given:

a = log 2/3

b = log 3/5

c = 2 log √(5/2)

To find:

${5}^{(a + b + c)} \: \: ---(1)$

Solution:

$c = 2 \log \sqrt{\frac{5}{2}} \\ \\ c = \log{ (\sqrt{ \frac{5}{2} }) }^{2} \\ \\ c = \log \frac{5}{2}$

Now, Putting the value of a, b and c in (1),

${5}^{(a + b + c)} \\ \\ = {5}^{( \log \frac{2}{3} + \log \frac{3}{5} + \log \frac{5}{2})} \\ \\ = {5}^{ \log( \frac{2}{3} \times \frac{3}{5} \times \frac{5}{2}) } \\ \\ = {5}^{ \log1} \\ \\ = {5}^{0} \\ \\ = 1$

So, The required answer is 1

Important Log Formula

$\log x+\log y = \log xy \\ \\ </p><p>2 \log x = \log x{}^{2} \\ \\ </p><p>\log 1 = 0 \\ \\ {x}^{0} = 1 \\ \\ [\text{Where all variables and base are real and > 0}]$