Question

Calculate logₓ ¹/2((x¹/2)(x ¹/4)(x ¹/8)(x ¹/16)).
a) 1
b) 2
c)−1 /2
d)−1

Answer 1

To calculate
`logₓ ¹/2((x¹/2)(x ¹/4)(x ¹/8)(x ¹/16))` , the expression can be simplified and then solved to get the answer as
`15/32` .

Step-by-step explanation:

To calculate
`logₓ ¹/2((x¹/2)(x ¹/4)(x ¹/8)(x ¹/16))` we can simplify the expression.

Since we have the logarithm base x, we can use logarithmic properties to rewrite the expression as,

`logₓ ((x¹/2)(x ¹/4)(x ¹/8)(x ¹/16))` to the power of
`1/2`.

Now, we can combine the exponents inside the parentheses:

`1/2 * (1/2 + 1/4 + 1/8 + 1/16)` .

This simplifies to
`1/2 * (8/16 + 4/16 + 2/16 + 1/16) = 1/2 * 15/16 = 15/32`.

Therefore, the answer is
`15/32` .