Question

16*8^(2+3x)=1

Answer 1

16*8^(2+3x)=1
2^4*2^3(2+3x)=2^0
2^(4+3(2+3x))=2^0
(4+3(2+3x))=0
4+6+9x=0
9x=-10
x=-10/9

Answer 2

To solve the equation 16 * 8^(2 + 3x) = 1, we'll follow these steps:

Step 1: Simplify the equation Step 2: Solve for x

Let's go through each step:

Step 1: Simplify the equation

We can simplify the equation by applying the exponent rule that states a^(b + c) = a^b * a^c.

16 * 8^(2 + 3x) = 1

Since 16 is a power of 2 (2^4), we can rewrite it as:

(2^4) * 8^(2 + 3x) = 1

Using the exponent rule, we have:

2^(4 * (2 + 3x)) = 1

Simplifying further:

2^(8 + 12x) = 1

Step 2: Solve for x

To solve for x, we'll take the logarithm of both sides of the equation with base 2. This will allow us to eliminate the exponent.

log2(2^(8 + 12x)) = log2(1)

Using the logarithm rule log_a(a^b) = b, we have:

(8 + 12x) * log2(2) = 0

log2(2) is equal to 1, so the equation becomes:

8 + 12x = 0

Next, we'll isolate the variable x by subtracting 8 from both sides:

12x = -8

Finally, divide both sides by 12 to solve for x:

x = -8/12

Simplifying the fraction:

x = -2/3

Therefore, the solution to the equation 16 * 8^(2 + 3x) = 1 is x = -2/3.