Question

Can someone please let me know the answer?

Answer 1

To find the value of
`16^(x)` given the equation
`2^(x+1) = 6`, we can use the fact that 16 can be expressed as
`2^(4)`. By substituting this into the expression we want to evaluate, we get:

`16^(x) = (2^(4)) ^(x) = 2^(4x)`

Now, let's substitute this expression into the given equation:

`2^((x+1)) = 6`

Replace
`2^((x+1))` with
`2^(4x)`

To find the value of x, we can take the logarithm of both sides. Let's use the natural logarithm (ln):

`ln(2^(4x)) = ln(6)`

Using the logarithmic property
`a.log_(b)(c) = log_(b)(c^(a))`, we can bring down the exponent:

4x⋅ln(2)=ln(6).

Now, solve for

`x=(ln(6))/(4.ln(2))`

Now that we have the value of x, substitute it back into the expression
`6^(x) = 2^(4x)` :

`6^(x) = 2^(4x) = 2^{4.(ln(6))/(4.ln(2)) }`

Simplify the expression:

`6^(x) = 2^(ln(6)/ln(2))`

Now, use the property
`a^{log_(a)(b) } = b`

`6^(x) = 6`

Therefore, the value of is
`6^(x) = 6`.