Solving Log Equations

Product Rule: log_a(m*n) = log_am+log_an

Quotient Rule: log_a(m/n) = log_am-log_an

Exponent Rule: y*log_a(m) = log_a(m^y)

If log_a(x) = log_a(y), the x = y

So log(x) = log(7), this means that x = 7

Recall we had a very similar rule when solving exponentials, b^x = b^y, x = y, why does it make sense that we have a similar rule?

Step 1) Use log rules and arithmetic to make it so there's only one log per side: log₄(7x) = log₄(35)

Step 2) Use the Equality Rule to set the insides equal to each other: 7x = 35

Step 3) Solve! x = 5