Question

Solve the following logarithmic equations. log2(49x^2) = 4

Answer 1

Answer:

$x_{1} = \frac{4}{7} \\x_{2} = \frac{-4}{7}$

Step-by-step explanation:

To solve this equation, one must apply the following logarithmic property:

if

$log_{a}(b) = c$

then

$b= a^{c}$

Applying it to the problem at hand:

$2^{4} = 49x^{2} \\x^{2} = \frac{16}{49} \\x_{1} = \frac{4}{7} \\x_{2} = \frac{-4}{7}$

The solutions to the problem are 4/7 and -4/7.

*Note that this solution was pretty straight forward because log2(16) = 4 is a known value, otherwise, a change of base to a base ten log would be required.