![]() ![]() So now we could say this exponent needs to be equal to that exponent because we have the same base. In fact, we could just say, "Look." Now I'm having trouble Now we just have to simplify a little bit. Is going to be equal to what we've had on the right-hand side, five to the two-x plus five. Minus in a neutral color, minus 18 minus two-x. So I could just subtract "this blue exponent from this yellow one." So, the left-hand side will simplify to five to the four-x plus three minus, let me just do Or we could say, "Hey, look I have five "to some exponent divided by five "to some other exponent, Sides of this equation by five to the 18 minus two-x. Two times nine is 18, two times negative-x is negative two-x, and that is going to be equal to, that is going to be equal to five to the two-x plus five. To the four-x plus three over five to the. Now five to the second, and then that to the nine minus x. Is going to be equal to five to the two-x plus five. So, we can rewrite this as five to the four-x plus three over, instead of 25, I could rewrite that as five-squared, and then I'm gonna raise that to the nine minus x, to the nine minus x, and that, of course, Yeah, 27 minus 12,Įight to the 15th power. Power, is the same thing as eight to the 27 minus 12th power. ![]() X back in there, you would get 32 to the 27 divided by 3, so 32 to the ninth And we are left with x is equal to, what is this going to be, 27. And now we can subtract nine-x from both sides, and so we will get five-x minus nine-x is gonna be negative four-x is equal to negative 108. So if we multiply everything times three, here we're going to get five-x is equal to nine-x minus. Let's see, we could, we could multiply, we could multiply everything by three. So five-x over three is equal to three-x minus 36. So, let's set them equal toĮach other and solve for x. Five-x over three must be equal to three-x minus 36. I have two to this power is equal to two to that power. So, two to the three-x minus 36, and now things have simplified nicely. And that's going to be equal to two to the. Left-hand side as two to the five-x over three, five-x over three power. Now if I raise something to a power, and then raise that to a power, I could just multiply these exponents. So, I can rewrite our original equation, as, instead of writingģ2, I could write it as two to the fifth, and then that's going to be raised to the x over three power, X over three power, is equal to, instead of writing eight, I could write two to the third power, two to the third power, and I'm raising that to the x minus 12, x minus 12. Two to the fifth power, two to the fifth power, and eight is the same thingĪs two to the third power, two to the third power. Integer power of eight." But, they are both powers of two. And when you look at it, you're like, "Well, 32 is not a power of eight, "or at least it's not an And you might first notice that on both sides of the equation And like always, pause the video and see if you can solveįor x in both of them. If you see inaccuracies in our content, please report the mistake via this form.Get even more practice solving some exponential equations, and I have two differentĮxponential equations here. If we have made an error or published misleading information, we will correct or clarify the article. Our editors thoroughly review and fact-check every article to ensure that our content meets the highest standards. Our goal is to deliver the most accurate information and the most knowledgeable advice possible in order to help you make smarter buying decisions on tech gear and a wide array of products and services. ZDNET's editorial team writes on behalf of you, our reader. Indeed, we follow strict guidelines that ensure our editorial content is never influenced by advertisers. ![]() ![]() Neither ZDNET nor the author are compensated for these independent reviews. This helps support our work, but does not affect what we cover or how, and it does not affect the price you pay. When you click through from our site to a retailer and buy a product or service, we may earn affiliate commissions. And we pore over customer reviews to find out what matters to real people who already own and use the products and services we’re assessing. We gather data from the best available sources, including vendor and retailer listings as well as other relevant and independent reviews sites. ZDNET's recommendations are based on many hours of testing, research, and comparison shopping. ![]()
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