Question

$8^x{} .16^{x-1} =1$

Answer 1

Question :-

${8}^{x} . {16}^{x - 1} = 1$

To Find:-

• x

Here, (.) represents (×)

${8}^{x} \times {16}^{x - 1} = 1$

Let us express the bases as primes with powers.

$( {2^{ 3} })^{x} \times { {(2}^{4}) }^{x - 1} = 1$

As we know that,

${( {a}^{m}) }^{n} = {a}^{m \times n}$

'a' being a whole number.

${2}^{3 \times x} \times {2}^{4(x - 1)} = 1$

${2}^{3x} \times {2}^{4x - 4} = 1$

By using the exponent law,

${a}^{m} \times {a}^{n} = {a}^{m + n}$

Here,

• a = 2

${2}^{3x + 4x - 4} = 1$

${2}^{7x - 4} = 1$

The only possible way that 2 power any number is equal to 1, is when the power is 0.

${a}^{0} = 1$

Hence, By taking the powers alone,

$7x - 4 = 0$

$7x =4$

$x = \dfrac{4}{7}$

Therefore in order to be LHS = RHS, x takes a value of 4/7.

Hope it helps

Happy day!

Answer 2

Step-by-step explanation:

1. Benzyl alcohol is fragrance and flavor material that also has preservative qualities. ... Although the term “alcohol” is used in the name, it does not contain any ethanol, the volatile alcohol found in alcoholic beverages and mouthwash products, and may be present in products that are considered alcohol free.