Evaluate the following expression without using a calculator. Use properties of

Question

Evaluate the following expression without using a calculator. Use properties of logarithms to expand the logarithmic expression as much as possible. Evaluate logarithmic expressions without using a calculator if possible. log_b(x^2y/z^2) = Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expression. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The solution set is (Type an exact answer in simplified form.) There is no solution.

Explanation / Answer

1) log2(sqrt2)

log2^1/2 / log2

= (1/2)[log2/log2]

= 1/2

2) logb(x^2y/z^2)

Use the property : log(x*y/z) = logx +logy -logz

So, logb(x^2y/z^2)

= logb(x^2) + logb(y) - logbz^2

= 2logb(x) + logb(y) - 2logb(z)

3) log2(x -4) = -4

(x-4) = 2^-4

x-4 = 1/16

x= 4+1/16 = 65/16

x= 65/16

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