Tutor profile: Luis E.

Solve the following equation: $$ 2^{x+1} = 100 $$

To solve the problem we must take the logarithm with a base of 2 on both sides: $$ log_{2}(2^{x+1}) = log_{2}(100) $$ Because of the rule of logarithms, taking the log of something with the same base as the base of the exponential cancels out the exponential part: $$ x+1 = log_{2}(100) $$ Next we can isolate x by subtracting one on both sides: $$ x = log_{2}(100) - 1 $$ or x is approximately 5.64385618977

A 12 V DC source is connected to a 100 Ohm and a 5 Kilo Ohm in series. What is the current flowing through the circuit?

There is approximately 2.4 mA flowing through the circuit.

$$ 2X - 5(X+1) = 6X + 5 $$ $$Solve for X$$

In order to solve a tricky looking problem like this, we need to follow the order of operations, AKA "P.E.M.D.A.S" Where: P - Parentheses E - Exponents M - Multiplication D - Division A - Addition S - Subtraction In this list, operations have ranks like in a deck of cards. Some operations have the same rank, for example, Multiplication and division have the same rank. Addition and subtraction also share the same rank. When presented with a situation where all the operations share the same rank we simply do the operations from left to right. For example: $$ 7\div5 * 2 * 5 $$ In this case we divide seven by five and then perform the multiplication. Now that we understand the order of operations we can solve this algebra problem $$ 2X - 5(X+1) = 6x + 5 $$ Following PEMDAS we first multiply the 5 and (X+1) $$ 2X - (5X + 5) = 6X + 5 $$ You may be wondering, what to do with that minus sign in front of that parentheses? Well believe it or not we are multiplying a -1 to (5X+5)! So we get, $$ 2X - 5X - 5 = 6X + 5 $$ Now we must combine like terms. This means that we add X's with X's and normal numbers with normal numbers: So, $$ -3X - 5 = 6X + 5 $$ Now we must get X by itself to solve the problem. There are several ways to do this step, I prefer to have less negative signs in my problems so I will add 3X on both sides. If you do an operation one side of the equals sign, you must do it to the other or the equation will not be true anymore $$ -5 = 9X + 5 $$ We can move the +5 to the other side by subtracting 5 on both sides $$ -10 = 9X $$ The last thing keeping us from knowing what X is, is the 9 in front. In algebra, having a number in front of a variable or letter means multiplication. for example 2X means $$ 2*X $$ ( We do not use 'x' for multiplication in algebra because x is the usual variable and It's hard to tell them apart) Knowing that 9 is being multiplied by X, we can divide both sides by 9 in order to have X all by itself. $$ \frac{-10}{9} = X $$ WAIT, we are not done yet! We should always check our work to make sure it is correct Let's see: $$ -10 = 9(\frac{-10}{9}) $$ The nines cancel out and we are left with $$ -10 = -10 $$ So our solution is correct!