In Exercises 51–58, solve each equation. Express the solution in ...

Question

In Exercises 51–58, solve each equation. Express the solution in scientific notation.

(2X10⁻⁵)x = 1.2X10⁹

Accepted Answer

Welcome back. I am so glad you're here. We're given this practice problem. It says for the following equation work out the value of X, right. The final answer in scientific notation, the equation that we're given is parentheses five times 10, raised to the negative fourth and parentheses times X equals 3.5 times 10 to the set. And the answer choices were given our a 7. times 10 to the 10th. B 7.0 times 10 to the 11th. C 1.43 times 10 to the 10th and D 1.43 times 10 to the 11th. I want to point out here that the X that we're solving for is this variable right in front of the equal sign. On the left hand side, the other exes are denoting multiplication. So to get that X by itself, it's being multiplied by that five times 10 to the negative fourth. And now we can divide both sides by the five times 10 to the negative fourth. That will get that X by itself, it will be absolutely thrilled. So on the left, those five times 10 to the negative fourths cancel out. And we've just got X on the right hand side, we have a fraction we have in the numerator 3.5 times 10 to the seventh and in the denominator five times 10 to the negative fourth. Now we are dividing these two things so we can divide the parts that are alike. So we can divide this 3.5 by five. And when we divide 3.5 by five, that gives us 0.7. And now we have these times tend to the various exponents. Well, the bases are the same, there are 10. And we recall from previous lessons that when we have the same bases that are being divided, we're going to subtract their exponents. So we're taking seven minus negative four, which is the same as seven plus four and seven plus four is 11. So this is 0.7 times 10 raised to the 11th power. Well, we almost have our final answer, but this is not in scientific notation yet. We recall from previous lessons that for scientific notation, we need one number to the left of the decimal point that has to be between one and nine zeros, not between one and nine. So it doesn't work. So we're going to need to move this decimal one to the right When we move our decimal place to the right, our exponent for the 10 to the is going to lower and it lowers by however many units we move the decimal. In this case, we move the decimal one unit to the right. So we're going to subtract one from our exponent of 11. Well, 11 -1 is 10. So this will be 7.0 times 10, raised to the 10th power. And there is our answer in scientific notation. We look at our answer choices for 7.0 times 10 to the 10th and that matches with answer choice a well done. We'll catch you on the next one.

In Exercises 51–58, solve each equation. Express the solution in scientific notation. (2X10⁻⁵)x = 1.2X10⁹

Key Concepts

Scientific Notation

Solving Exponential Equations

Properties of Exponents

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