Solving Exponential Equations with Like Bases
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- Math in Music Now that we have an understanding of what an exponential function is, we're going to look at a specific use of exponential equations in music. If you've ever liste…
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- Now that we've learned about exponential growth and exponential decay, we can learn how to solve exponential equations. We'll then move into asymptotes and graphing exponential …
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Problems 30
- Solve for xxx. 63x=36x+16^{3x}=36^{x+1}63x=36x+1
- Solve for xxx. 25−2x=56x−325^{-2x}=5^{6x-3}25−2x=56x−3
- Solve for xxx. 42x2x−3 =1\frac{4^{2x}}{2^{x-3}}\ =12x−342x =1
- Solve for xxx. 31−x3x =95x\frac{3^{1-x}}{3^{x}}\ =9^{5x}3x31−x =95x
- A group of bacteria was observed to be at 130013001300 and grow at a rate of about 3.52%3.52\%3.52% per day. What is an equation for the bacteria's growth? How long will it take…
- A species of fish has an extremely long lifespan and rarely have children. If there are a total of 930930930 of this type of fish and their growth rate is 8.3%8.3\%8.3% each mon…
- A type of bacteria has a very high exponential growth rate of 76%76\%76% every hour. If there are 101010 bacteria, determine how many there will be in half a day. How long until…
- An island was recorded to have a population of 100100100 after 222 years. Then, after 666 years, it was recorded to have a population of 810081008100. Find the equation that rep…
- In 200820082008, Cooper bought a car for 36000\3600036000. It depreciates 12%12\%12% per year. What year will the car be worth 6000\60006000?
- The half-life of an isotope is 333 years. how many years would it take a 101010 mg sample to decay to 0.50.50.5 mg? Round to the nearest year.
- If 400400400 mg of ibuprofen decreases about 30%30\%30% every hour, how long would it take for 424242 mg to remain?
- If 6951.37\6951.376951.37 was put into your account at some unknown date and it's now 10166.30\10166.3010166.30. The interest rate is 7.7%7.7\%7.7% and it is compounded triannua…
- An unknown amount of money was placed in a bank account with a semiannual interest rate of 8.8%8.8\%8.8%. After 333 years, there's 3545.17\3545.173545.17 in the account. After t…
- An isotope decays exponentially. Suppose that after one minute, there are 101010 grams remaining, and after five minutes, there are 222 grams remaining. What is the half-life, i…
- Solve for xxx: 551−550−54919=5x.\frac{5^{51}-5^{50}-5^{49}}{19} = 5^x.19551−550−549=5x.
- Solve for xxx: 9(3)x−1=81x−2.\frac{9}{(\sqrt{3})^{x-1}} = 81^{x-2}.(3)x−19=81x−2. Write your answer as a fraction in simplest form, without spaces.
- Solve for kkk: 32018+32017−32016−32015=k⋅320153^{2018} + 3^{2017} - 3^{2016} - 3^{2015} = k \cdot 3^{2015}32018+32017−32016−32015=k⋅32015
- About how many people are needed to guarantee that one person will answer all the questions correctly and win the prize?
- Solve for xxx: 4250(−8)6x=(−2)5254^{250}(-8)^{6}x = (-2)^{525}4250(−8)6x=(−2)525
- If Earth has approximately 7.67.67.6 billion people, how many times would Thanos have to snap for there to be 111 person left? Round your answer to the nearest whole number.
- Solve for xxx. 27x36x−1 =1\frac{27^{x}}{3^{6x-1}}\ =136x−127x =1
- Solve for xxx: 92x−1=34x−19^{2x-1}=3^{4x-1}92x−1=34x−1
- Solve for xxx: 94x−2=32x−19^{4x-2}=3^{2x-1}94x−2=32x−1
- Solve for xxx: 92x−1=34x−29^{2x-1}=3^{4x-2}92x−1=34x−2
- Solve for bbb: y=bxy=b^xy=bx (assuming all variables represent positive numbers).
- Solve for xxx: y=bxy=b^xy=bx (assuming y>0y>0y>0, and b>1b>1b>1).
- Find relatively prime integers aaa and xxx such that: 300=a(5)x300=a(5)^x300=a(5)x
- Solve for xxx: 72=576(12)x72=576(\frac{1}{2})^x72=576(21)x
- Let f(x)=2x8f(x)=2x^8f(x)=2x8 and g(x)=7x3g(x)=7x^3g(x)=7x3. Find h(x)=g(x)f(x)h(x)=\frac{g(x)}{f(x)}h(x)=f(x)g(x).
- Which of the following are solutions for a,b,c,d,e,a, b, c, d, e,a,b,c,d,e, and fff (in order)? Select all that apply.