Properties of powers

[emilys]

I am able to find the answer to this problem using a graphing calculator, however I must solve it algebraically and once I get to a certain point I am unsure what to do. this is what I have so far: the problem is

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2^x+3 +15=70

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2^X+3 =55

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after this point I am unsure how to transfer the 2 to the other side. Please help me!!

 

[HallsofIvy]

I am able to find the answer to this problem using a graphing calculator, however I must solve it algebraically and once I get to a certain point I am unsure what to do. this is what I have so far: the problem is

---

2^x+3 +15=70

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2^X+3 =55

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after this point I am unsure how to transfer the 2 to the other side. Please help me!!

You don't "transfer the 2 to the other side". You reverse the "\(\displaystyle 2^x\)" function by using its inverse function, the logarithm function. So strictly speaking, from \(\displaystyle 2^{x+ 3}= 55\) we get \(\displaystyle x+ 3= log_2(55)\) and then \(\displaystyle x= log_2(55)- 3\).

Of course, your calculator probably does not have a "logarithm base 2" key (some do!) but it should have logarithm base 10 (common log) or base e (natural log) and any logarithm has the property that \(\displaystyle log(a^b)= b log(a)\). So whatever base you use, \(\displaystyle log(2^{x+ 3})= (x+ 3)log(2)= log(55)\).