Question

Log8X=2 and Log6Y=3. Find Log8 (X+Y)?​

Answer 1

Given:

• $log_{8}X=2,\quad log_{6}Y=3$

To find:

• $log_{8}(X+Y)$

Solution:

• Now, $log_{8}X=2$

• $\Rightarrow \frac{logX}{log8}=2$

• $\Rightarrow logX=2\:log8$

• $\Rightarrow logX=log(8^{2})$

• $\Rightarrow logX=log64$

• $\Rightarrow X=64$

• and $log_{6}Y=3$

• $\Rightarrow \frac{logY}{log6}=3$

• $\Rightarrow logY=3\:log6$

• $\Rightarrow logY=log(6^{3})$

• $\Rightarrow logY=log216$

• $\Rightarrow Y=216$

• Now, $log_{8}(X+Y)$
• $=log_{8}(64+216)$
• $=log_{8}(280)$

Answer: $log_{8}(X+Y)=log_{8}(280)$

Remember:

• $log_{a}(b)=\frac{log_{c}(a)}{log_{c}(b)}$