Question

Which of the following shows the true solution to the logarithmic equation 3 log Subscript 2 Baseline (2 x) = 3 x = negative 1 x = 1 x = negative 1 and x = 1 x = 0, x = negative 1, and x = 1.

Answer 1

The equation which shows the true solution to the given logarithmic equation is,

$x=1$

What is power rule of logarithmic function?

The power of the log rule says that the number written in the front of the logarithmic function can be raised to the power of the logarithmic function.

For example,

$n\log_b(M)=\log_b(M)^n$

Given information-

The logarithmic equation given in the problem is,

$3\log_2(2x)=3$

Using the power rule of the logarithmic function,

$\log_2(2x)^3=3$

Using the exponent rule of the logarithmic function the above equation can be written as,

$(2x)^3=3$

Solve it further,

$8x^3=3\\x^3=1\\x=1$

Hence, the equation which shows the true solution to the given logarithmic equation is,

$x=1$

Learn more about the rules of logarithmic function here;

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