Question

SOLVE THE GIVEN EXPONENTIAL EQUATIONS .

ANSWER CORRECTLY​

Answer 1

16

Step-by-step explanation:

$( \sqrt{2} ) ^{x} = {2}^{8}$

$2 {}^{ \frac{1}{2} \times x } = {2}^{8}$

$2 ^{ \frac{x}{2} } = {2}^{8}$

comparing power both sides we get,

x/2 = 8

x = 8×2

x = 16

Answer 2

Question :

Solve for x : $\tt {\sqrt{2}}^{x} = {2}^{8}$

Solution :

$\tt {\sqrt{2}}^{x} = {2}^{8}$

$\tt \implies {2}^{\frac{x}{2}} = {2}^{8}$

$\tt \implies \frac{x}{2}$ = 8

$\tt \implies$ x = 8 × 2

$\tt \implies$ x = 16

x = 16

Properties of indices

● $\tt {x}^{a}×{x}^{b} = {x}^{a+b}$

●$\tt {x}^{a}÷{x}^{b} = {x}^{a-b}$

●$\tt {({x}^{a})}^{b} = {x}^{ab}$