Q&A for How to Solve Exponential Equations

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What do I do with the exponents when the bases are the same?

David Jia
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Expert Answer

Whenever you're solving exponents and the bases are the same, you can add the exponents together. If you have x^2 times x^3, you would add the exponents together and get x^5.

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How do I calculate 1.025 base number (exponent) to power 12 easily?

Donagan

Top Answerer

Manually, there is no easy way to do this. The only easy way is to use a calculator with an exponent function (often shown by the symbol "^").

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Question

I made a formula -1+2^n=X to find the maximum number countable with so many digits in binary. How do I turn it around to find the number of digits for a certain number? I want to input x to find n.

Community Answer

OK, you can rearrange to have 2^n = X+1. Then take logs of both sides. log (2^n) = log (X+1). Then you can use properties of logs to get n*log2 = log(X+1) and solve for n = log(x+1)/log2. That's not quite what you want because you need the formula to return whole numbers for n, but you can fix that by saying n = ceil(log(X+1)/log2) where ceil is the rounding up function. Everything here works no matter what base you do the logarithms in (as long as you use the same base for them all), but do them in base 2 if you can because then the formula reduces to n = ceil(log_2 (X+1)).

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Question

How do I solve 2^5/2 - 2^3/2?

Donagan

Top Answerer

2^5/2 is √(2^5), or √32 = 5.66. 2^3/2 is √(2³), or √8 = 2.83. 5.66 - 2.83 = 2.83.

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What is of a¾ = 81?

Donagan

Top Answerer

To solve for "a," raise 81 to the power of 4/3. That is, raise 81 to the fourth power, then find the cube root of that number. 81^4 = 43,046,721. The cube root of 43,046,721 = 350.467. That's "a."

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Question

I still can't understand how x-4=5 could be made into x=5+4? It's confusing me a lot.

Verin

Top Answerer

All that's happening is that 4 is being added to both sides of the equation. On the left side, we x - 4 + 4, which equals x, and on the right side, we get 5 + 4, which equals 9. Thus, the full equation becomes x - 4 (+ 4) = 5 (+4), which simplifies to x = 9. The 4 must be added to both side to maintain the equality.

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How can I solve 4(4^x – 2^x) + 1 = 2^x?

Community Answer

Distribute the 4 then take the natural log of both sides and isolate the x to get your answer.

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