Question

Solve this problem
need fast

`{6}^(x + 3) = √(6)`

​

Answer 1

x=-5/2

Explanation:

Hi there!

We are given the following equation:

`6^(x+3) = √(6)`

We want to find the value of x

This is an exponential equation. In order to find the value of x, we need to make sure that both sides of the equation are at the same bases before we solve the equation

On the left side, we have 6 (the base) raised to the power of x+3

On the right, we have √6

Here's a trick to make this problem easier: the square root of a number is equal to that number, raised to the power of 1/2. In other words, √a is equal to
`a^(1)/(2)`

Therefore, √6 is equal to
`6^(1)/(2)`

Rewriting the equation then:

`6^(x+3)=6^(1)/(2)`

Both sides have the same base (6)

Now we can solve the equation for x. Simply take what the exponents are, and then set them equal to each other.

This means:

x + 3 = 1/2

Subtract 3 from both sides

x+3=1/2

-3 -3
___________

x = -5/2

Hope this helps!