Summarize the following:
Make sure that there is an exponential expression on one side of the equation, and a whole number on the other side. If not, you need to rework the equation so that the exponent is alone on one side. For example, if your are trying to solve 3x52=79{\displaystyle 3^{x-5}-2=79}, you first need to isolate 3x5{\displaystyle 3^{x-5}} by adding 2 to each side of the equation:3x52=79{\displaystyle 3^{x-5}-2=79}3x52+2=79+2{\displaystyle 3^{x-5}-2+2=79+2}3x5=81{\displaystyle 3^{x-5}=81} You need to determine whether the whole number can be converted to an exponent with the same base as the other exponent. If you can't convert the whole number in this way, you cannot use this method. For example, look at the equation 3x5=81{\displaystyle 3^{x-5}=81}. You need to change 81 to an exponent with a base of 3, so that it matches the other exponential expression in the equation. By factoring out 3, you should see that 3333=81{\displaystyle 3 imes 3 imes 3 imes 3=81}, so 34=81{\displaystyle 3^{4}=81}. The new equation then becomes 3x5=34{\displaystyle 3^{x-5}=3^{4}}. Since you converted the whole number, you now have two exponential expressions with the same base. Since the bases are the same, you can ignore them and focus on the exponents. For example, since 3x5=34{\displaystyle 3^{x-5}=3^{4}} has two exponents with a base of 3, you can ignore the base and simply look at the equation x5=4{\displaystyle x-5=4}. To do this, you need to isolate the variable on one side of the equation. Make sure that whatever you do to one side, you also do to the other side. For example:x5=4{\displaystyle x-5=4}x5+5=4+5{\displaystyle x-5+5=4+5}x=9{\displaystyle x=9} You can see if your answer is correct by plugging the solution you found back into the original equation. After simplifying each expression, both sides of the equation should be equal. If they aren't, you miscalculated and need to try again. For example, if you found that x=9{\displaystyle x=9}, you would plug in 9{\displaystyle 9} for x{\displaystyle x} in the original equation and simplify:3x5=81{\displaystyle 3^{x-5}=81}395=81{\displaystyle 3^{9-5}=81}34=81{\displaystyle 3^{4}=81}81=81{\displaystyle 81=81}

summary: Isolate the exponential expression. Rewrite the equation. Write the equation for the exponents only. Solve for the variable. Check your work.

Summarize the following:
That's the main reason of summer break! Relax and recharge. Summer will go by faster than you think! You won't have to wake up at the crack of dawn to catch the bus, so make up a couple of much needed hours of sleep. Go on and get your summer reading over with. You won't be cramming the week before, if you do it now. The days are longer now, so you have more sunlight to do more outdoor things.

summary: Relax. Sleep an extra hour, or so. Read. Go on bike rides, or go walking.

Summarize the following:
Insert the hook through the first stitch or space to be worked over. The hook should not be attached to any yarn yet. Note that the right side of the piece should face toward you but the yarn should be at the back. Grab the yarn with your hook. Pull both the yarn and hook through to the front of the piece. You should have one loop on your hook after completing this step. Insert the hook into the stitch or space directly next to the one you first worked in. Yarn over the hook from back to front. In one motion, pull the yarn-over back through to the front of the work while also pulling it through the loop previously on your hook. If this motion is too difficult for you to master, you can pull the yarn-over through to the front of the work first before pulling it through the loop on your hook. You've essentially just completed one chain stitch over the surface of the original piece, thereby securing the yarn in place. Insert the hook back into the second worked stitch and follow the same procedure to create another chain stitch. Repeat this as many times as needed to build the size dot you desire. For a moderately sized dot, create three to five of these stitches. Each of these chain stitches must be worked over the same stitch of your original piece. When you're satisfied with the dot size, insert the hook through the stitch or space directly next to the one your chain stitches were worked into. Yarn over the hook from back to front, then pull this yarn-over back through to the front of the work while simultaneously pulling it through the loop already on your hook. As before, you can pull the yarn-over through to the front of the work before pulling it through the loop if doing so is easier for you. This final chain stitch closes the dot. Cut the yarn, leaving a 4-inch (10-cm) tail. Pull this tail through the loop on your hook to finish and secure the stitch. Pull the loose tail of yarn back through to the back of the work and weave it into the underside of the piece to hide it. This step also provides the dot with further security.
summary: Insert the hook. Draw up a loop. Insert the hook into the next stitch. Chain one through the stitch. Repeat several times. Insert the hook into the next stitch. Chain one. Fasten off the yarn.