What is the value of b in this math equation?

Question

Ok... the equation is 4^2b-3=8^1-b

What is the value of b?

-3/7

7/9

9/7

10/7

Answer 1

4 = 2^2
8 = 2^ 3
4^(2b-3) = 2^(4b-6)
8^(1-b)=2^(3-3b)
4b-6 = 3-3b
7b= 9
b = 9/7

Answer 2

Let's use a logarithmic expression to solve for 'b'. Let's use a logarithm with a base of '2'.

Now, after taking the logarithm base 2 of both sides we get:

(2b - 3)log (base 2) of 4 = (1-b)log (base 2) of 8

The answer to the logarithmic expression on the left side of the above equation is the integer '2', and on the right side of the above equation is the integer '3'. This is because 2 squared equals 4 and 2 cubed equals 8, where squared means 2 to the second power and 2 cubed means 2 to the third power.

Now, we have (2b - 3)*2 = (1 - b)*3

This a simple algebraic expression now.

4b - 6 = 3 - 3b

Add '3b' and the integer '6' to both sides of the equation:

7b =9

Divde both sides of the equation by the integer '7' and the result is 9/7.

Answer 3

7

Answer 4

9/7

4 is 2^2 and 8 is 2^3... if you reduce 4 and 8 to 2 and multiply the exponents by 2 and 3, respectively, you can solve the exponents for b as though it was a normal algebraic equation.

Answer 5

[02]
4^(2b-3)=8^(1-b)
2^2(2b-3)=2^3(1-b)
2^(4b-6)=2^(3-3b)
Now as the base on the both sides are equal,the expnents must be equal
4b-6=3-3b
4b+3b=3+6
7b=9
b=9/7 ans