Question

What is the solution to 4 superscript log subscript 4 baseline (x 8) baseline = 4 squared

Answer 1

The solution to 4 superscript log subscript 4 baseline (x 8) baseline = 4 squared for the variable x is 8.

What is the exponent of log rule?

The exponent of the log rule says that the raising a logarithm with a number to its base is equal to the number.

For example, let k is the number and a is the base. Thus,

$a^{\log a(k)}=k$

The logarithmic equation given in the problem is,

$4^{\log_4(x+8)}=4^2$

Compare the equation with the expression of exponent of log rule, we get,

$x+8=4^2\\x+8=16\\x=16-8\\x=8$

Thus, the solution to 4 superscript log subscript 4 baseline (x 8) baseline = 4 squared for the variable x is 8.

Learn more about the rules of logarithmic function here;

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