How do you solve #7^ { x - 2} = 343#?

1 Answer
shr
Oct 30, 2016

5

Explanation:

How do we know this? Well for exponents we must create the same base before we can solve the equation. 7 itself is 7 to the power of one, whereas 343 is 7 to the power of 3. Now we can recreate the equation like this:

#7^(x-2)=7^3#

Now the exponents have the same base, which means we can ignore the bases, and look at the exponents. In the exponents, we can state:

#x-2 = 3#
Therefore, #x = 5#

Remember it is always essential to create the same base to solve exponent problems like this. Also note that when a value is equal to one, anything to the power of 0 is one. Thus you can simply set the exponents equal to zero.

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