Question

How to solve log8+3√7 base of 8-3√7

Answer 1

Answer:

- 1

Step-by-step explanation:

$\sf log_{(8 - 3 \sqrt{7} )}8 + 3 \sqrt{7}$

$\Rightarrow \sf log_{(8 - 3 \sqrt{7} )}8 + 3 \sqrt{7}$

Multiplying and dividind 8 + 3√7 by 8 - 3√3

$\Rightarrow \sf log_{(8 - 3 \sqrt{7} )} \dfrac{(8 + 3 \sqrt{7})(8 - 3 \sqrt{7)} }{8 - 3 \sqrt{7} }$

$\Rightarrow \sf log_{(8 - 3 \sqrt{7} )} \dfrac{ {8}^{2} - (3 \sqrt{7} )^{2} }{8 - 3 \sqrt{7} }$

$\Rightarrow \sf log_{(8 - 3 \sqrt{7} )} \dfrac{ 64- 63 }{8 - 3 \sqrt{7} }$

$\Rightarrow \sf log_{(8 - 3 \sqrt{7} )} \dfrac{ 1 }{(8 - 3 \sqrt{7})^{1} }$

$\Rightarrow \sf log_{(8 - 3 \sqrt{7} )} (8 - 3 \sqrt{7})^{ - 1}$

$\Rightarrow \sf - 1 \times log_{(8 - 3 \sqrt{7} )} (8 - 3 \sqrt{7})$

$\Rightarrow \sf - 1$