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Relationship between exponentials & logarithms: graphs

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This article has also been viewed , times. Categories: Exponents and Logarithms. Learn more Method 1. Learn the correct words and vocabulary for exponent problems.

The bottom number, here a 2, is the base. The number it is raised to, here a 3, is known as the exponent or power. Multiply the base repeatedly for the number of factors represented by the exponent. If you need to solve an exponent by hand, start by rewriting it as a multiplication problem.

Higher Maths NAB 3 Outcome 3: Logarithmic functions

You want to multiply the base by itself for the number of the exponent. Solve an expression: Multiply the first two numbers to get the product. Start by multiplying the first two fours.

Multiply that answer to your first pair 16 here by the next number. Keep multiplying in the numbers to "grow" your exponent. Simply keep multiplying the first two numbers, then multiply the answer by the next number in the sequence. This works for any exponent. Try your hand with a few more examples, checking your answers with a calculator. The button is usually clearly labeled. The Windows Seven calculator tool can be changed to scientific calculator mode by clicking the "View" tab of the calculator and selecting "Scientific".

When you want the standard calculator mode back, use "View" and select "Standard".

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Google the expression to check your answer. Method 2. Add or subtract exponents only if they have the same base and exponent. Just add the number of similar terms with the identical base and exponent together and multiply the sum by that exponential expression. Multiply numbers with the same base by adding the exponents together. If you have an number raised to a power, and the whole thing is then raised to a power, simply multiply the two exponents.

Exponentials & Logs - Higher Mathematics

Again, think of what these symbols actually mean if you get confused. Treat negative exponents like fractions, or the number's reciprocal. If you don't know what reciprocals are, it is okay. Divide two numbers with the same base by subtracting the exponents. Division is the opposite of multiplication, and while they aren't always solved exactly opposite, they are here. Negative exponents create fractions.

Try out some practice problems to get use to manipulating exponential numbers.

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The following problems cover everything currently shown. To see the answer, simply highlight the entire line the problem is on. Method 3. Roots are the inverse of exponents. Turn the top number into a normal exponent for mixed fractions. Simply turn the base into a root, like a normal fraction, then raise the whole thing to the power on the top of the fraction.

Unsure about Exponentials & Logarithms?

If you're struggling to remember this, think through the theory. Add, subtract, and multiply fractional exponents just like normal. It is much easier to try and add and subtract your exponents before solving them or turning them into roots. If the base is the same and the exponent identical, you can add and subtract like normal. If the base is the same, you can multiply and divide the exponents like normal as well, as long as your remember how to add and subtract fractions.

The 3 is a root sign meaning you find the cube root. In this case you would square 3 -- which is 9 -- and then you find the cube root of 9. If you wanted to, you could reverse the order of those two operations by first finding the cube root of 3 and then squaring that number. In either case the answer would be the same. Yes No. Not Helpful 0 Helpful Four to the power of 2 is 16, since 4 times 4 is Not Helpful 5 Helpful Half exponents are square roots Why? Not Helpful 8 Helpful Not Helpful 4 Helpful 8. Can you help me solve this problem?