If 3^x = 3/5, find the value of 3^(x-3) 2. If 4^(9-2) = 3, find the value of 2^(29-3)
1. If 3^x = 3/5, find the value of 3^(x-3)
2. If 4^(9-2) = 3, find the value of 2^(29-3)
2. If 4^(9-2) = 3, find the value of 2^(29-3)
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info@snapandsolve.comGiven the equation 3^x = 3/5, we want to find the value of 3^(x-3).
First, we express 3^(x-3) using properties of exponents:
3^(x-3) = 3^x * 3^(-3)
Substituting the value of 3^x:
3^(x-3) = (3/5) * 3^(-3)
Calculating 3^(-3):
3^(-3) = 1/(3^3) = 1/27
Now substituting it back:
3^(x-3) = (3/5) * (1/27) = 3/(5 * 27)
Calculating the denominator:
5 * 27 = 135
So, the final answer is:
3^(x-3) = 3/135 = 1/45
Given the equation 4^(9-2) = 3, we want to find the value of 2^(29-3).
First, we simplify 4^(9-2):
4^(9-2) = 4^7 = 3
Since 4 = 2^2, we rewrite it:
(2^2)^7 = 2^(2*7) = 2^14
Thus, we have:
2^14 = 3
Next, we need to find 2^(29-3):
29 - 3 = 26
So we want to find 2^26. This can be expressed as:
2^26 = (2^14)^(26/14) = 3^(26/14)
Calculating 26/14:
26/14 = 13/7
Thus, we have:
2^26 = 3^(13/7)
So, the final answer is:
2^(29-3) = 3^(13/7)
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