Question Solve the following logarithm problem for the positive solution for z. log_(256)x=-(3)/(4) Answer Attemptiout of square

Question

Answer 1

To solve the logarithmic equation

, we need to convert it to its exponential form. The general form of a logarithmic equation

can be rewritten in exponential form as

.Given:

We rewrite this in exponential form:

Next, we simplify

. First, note that

can be expressed as a power of 2:

So, we have:

Using the property of exponents \((a^m)^n = a^{mn}\), we get:

Now,

is the same as

:

Therefore, the positive solution for

is:

So, the answer is:

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