Trying to figure out my percentage raises at work If I make $ 14.40 right now and max out at 24 an hour, how many seperate 2% raises will I need to get to be at the max? 
Is there a simple math equation to get this answer or do I have to just keep multiplying 2% to each new wage and then add up how many times it took?
 A: You are looking for a solution to the equation
$$14.4\cdot 1.02^x = 24$$
and here $\log_{1.02}$ yields the solution
$$x = log_{1.02} \left( \frac {24}{14.4} \right) \approx 25.796$$
edit: There was an error in my previous result, that has been corrected.
A: You want to solve the following equation for $n$:
$$14.40\times 1.02^n = 24.00$$
$$\ln(14.4\times1.02^n) = \ln(24)$$
Apply the rules to separate products and bring down the exponent
$$\ln(14.4) + n\ln(1.02) = \ln(24)$$
Subtract from both sides, then combine the logarithms
$$n\ln(1.02) = \ln(24) - \ln(14.4) = \ln\left(\frac{24}{14.4}\right)$$
Then divide by the remaining coefficient to isolate $n$:
$$n = \frac{\ln\left(\frac{24}{14.4}\right)}{\ln(1.02)} \approx 25.79$$
Which means it will take you $25$ raises to bring you just under the limit, and $26$ to go over.
A: If the wage of $\$ 14.4$ raises one time, the new wage is $\$ 14.4 \cdot 1.02$
If the wage of $\$ 14.4$ raises two times, the new wage is $\$ 14.4 \cdot 1.02^2
$
If the wage of $\$ 14.4$ raises n times, the new wage is $\$ 14.4 \cdot 1.02^n
$
Thus your equation is $\$ 14.4 \cdot 1.02^n=\$ 24$
Dividing both sides of the equation by $\$ 14.4$
$1.02^n=\frac{24}{14.4}$
Taking logs
$n\cdot \log(1.02)=\log\left( \frac{24}{14.4} \right)$
${\large{n=\frac{ \log\left( \frac{24}{14.4} \right)}{{\log(1.02)}}}}\approx 25.8$
Since you want to have at least $\$ 24$, you need 26 raises.
