27 root 3 =3^b. Find the value of b.
The cubed root of 27 is 3. So be will equal 3.
On the other hand, if you meant
27√3, that makes b=7/2
The way it is written, I must agree with Steve
To find the value of exponent b in the equation 27 root 3 = 3^b, we need to use logarithms.
First, let's rewrite the equation in a more familiar form:
27 root 3 = 3^b
Since 27 is equal to 3 raised to the power of 3 (3^3), we can substitute it into the equation:
(3^3) root 3 = 3^b
To simplify the left side, we need to understand that the nth root of x can be represented as x^(1/n). So, we can rewrite the equation as:
(3^3)^ (1/2) = 3^b
Using the exponent power rule, we can simplify the equation further:
3^(3 * 1/2) = 3^b
3^(3/2) = 3^b
Now, since the bases are the same (3), we can equate the exponents:
3/2 = b
Therefore, the value of b is 3/2, or 1.5.