1/2log4 7 + log4 32 - 1/2log4 28

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To simplify this expression, we can use the properties of logarithms:

1/2log4 7 + log4 32 - 1/2log4 28

First, we can use the power rule of logarithms to simplify the expressions involving exponents:

= log4(7^(1/2)) + log4(32) - log4(28^(1/2))

= log4(√7) + log4(32) - log4(√28)

Next, we can combine the logarithms using the product rule:

= log4(√7 * 32) - log4(√28)

= log4(√(7 * 32)) - log4(√28)

= log4(√224) - log4(√28)

Now, we can simplify the expressions under the square roots:

= log4(√(16 14)) - log4(√(4 7))

= log4(√16 √14) - log4(√4 √7)

= log4(4√14) - log4(2√7)

Finally, we can combine the two square roots and simplify:

= log4(4√14 / 2√7)

= log4(2)

Therefore, the simplified expression is log4(2).