MATH SOLVE

2 months ago

Q:
# arrange the steps in the correct order to solve the equation 3 (2^2t-5 )- 4=10

Accepted Solution

A:

The equation to be solved is: 3 [ 2 ^ (2t - 5) ] - 4 = 10

The steps are:

1) transpose - 4=> 3 [ 2^ (2t - 5) ] = 10 + 4

2) Combine like terms => 3 [2^ (2t - 5) ] = 14

3) Divide both terms by 3 => 2^ (2t - 5) = 14 / 3

4) Take logarithms of both sides => (2t - 5) log (2) = log (14/3)

5) Divide both sides by log (2) =>

log (14/3)

2t - 5 = -------------------

log (2)

6) transpose - 5+>

log (14/3)

2t = ------------------- + 5 = 2.22 + 5

log (2)

2t = 7.22

7) divide both sides by 2 => t = 7.22 / 2 = 3.61

The steps are:

1) transpose - 4=> 3 [ 2^ (2t - 5) ] = 10 + 4

2) Combine like terms => 3 [2^ (2t - 5) ] = 14

3) Divide both terms by 3 => 2^ (2t - 5) = 14 / 3

4) Take logarithms of both sides => (2t - 5) log (2) = log (14/3)

5) Divide both sides by log (2) =>

log (14/3)

2t - 5 = -------------------

log (2)

6) transpose - 5+>

log (14/3)

2t = ------------------- + 5 = 2.22 + 5

log (2)

2t = 7.22

7) divide both sides by 2 => t = 7.22 / 2 = 3.61