Question

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

Answer 1

`x_(1) = (4)/(7) \\x_(2) = (-4)/(7) \\`

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) = (16)/(49) \\x_(1) = (4)/(7) \\x_(2) = (-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.