Logarithmic Solutions: Unveiling x in a Numeric Equation with Base -10

Firstly, I'd like to add that logarithms are generally not used with negative bases, it's a bit outside of standard mathematical practice due to some tricky complex number complication. However, for the purposes of instruction and considering that you asked for it, I'll help you solve the equation. Beginning with your equation -2 * 10^4x = -300 we can first eliminate - sign from both sides: 2 * 10^4x = 300 Then divide both sides by 2: 10^4x = 150 The equation above is equivalent, in logarithmic form, to the following: 4x = log_base10(150) Then simplify to find x: x = (log_base10(150))/4. Now, if you want to approximate the value using a standard scientific calculator, you'll need to know that the normal "log" function on a calculator is base 10 logarithm, so: x = log(150) / 4 is ≈ 0.477, rounded to the nearest thousandth.