The value of y in the equation 5^y = 8.2^x - 5 if x is 8.2 is 10.2
The equation is given as:
5^y = 8.2^x - 5
The value of x is given as:
x = 8.2
So, we substitute x = 8.2 in the equation 5^y = 8.2^x - 5
So, we have:
5^y = 8.2^8.2 - 5
Evaluate the exponent 8.2^8.2
So, we have:
5^y = 31136772.215 - 5
Evaluate the difference of 31136772.215 and 5
So, we have:
5^y = 31136767.215
Take the logarithm of both sides
y * log(5) = log(31136767.215)
Divide both sides by log(5)
y = 10.72
Hence, the value of y in the equation 5^y = 8.2^x - 5 if x is 8.2 is 10.2
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Complete question
Given the equation 5^y = 8.2^x - 5. Determine the value of y if x is 8.2