Consider the equation 10 = 2^x
(a) Solve the equation for x by taking the common logarithm of both sides.
log10 = xlog2
x = log10/log2
(b) use the result to show that 10 = 2^1/log2
I understand that this works because log10 = 1, thus 1/log2 is the same thing as log10/log2. However, how does the power law of logarithm apply here? If i were to prove this question algebraically.
(c) apply algebraic reasoning to show that 10 = 3^1/log10
I get how this works in my mind, but i can't come up with an explanation, or the reasoning behind it.
Thank you for the help,