If two equivalent logarithmic expressions have the same base, then the arguments must be equal.
x = 16
Practice makes perfect
We want to solve an equation involving more than one logarithm. To do so, we will use the Change of Base Formula to evaluate the given equation.
log_b m = log_c m/log_c b
In the above formula, m, b, and c are positive numbers, with b≠1 and c≠1. We will apply this formula with c = 2 to simplify the expressions.
Next, we will use the fact that if two equivalent logarithmic expressions have the same base, then the arguments must be equal.
log_b x=log_b y ⇔ x= y
Let's apply the above property to our equation.
log_2 x^3 = log_2 (4x)^2
⇔
x^3 = (4x)^2
Let's now solve the equation x^3 = (4x)^2.
Note that you can never get zero by raising a number different from zero to any power, so both log_4 0, and log_8 0 are undefined. Therefore, 0 is an extraneous solution. Let's now check for x = 16.
