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Edufirst
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

Answer:

Below

Step-by-step explanation:

The equation: 3(2^2t-5)-4=10

1) Add 4 to each side of the equation --> 3(2^2t-5)=14

2) Divide both sides of equation by 3 --> (2^2t-5)=14/3

3) Take the log of each side --> log(2^2t-5)=log(14/3)

4) Use the Exponential Property and write 14/3 in decimal form -->                (2t-5)log2=log4.67

5) Divide each side by log 2 --> 2t-5 = log4.67/log2

6) Find the value of log4.67/log2 and substitute --> 2t-5=2.23

7) Add 5 to each side of the equation --> 2t=2.23+5

8) Simplify --> t=3.625

Sorry, no explanations.

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