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25^x = 250Take the natural log of both sides...x * ln(25) = ln(125 * 2)x * ln(25) = ln(125) + ln (2)x * 2ln(5) = 3ln(5) + ln(2)Divide both sides by 2ln(5)x = 3/2 + ln(2)/2ln(5)Clean it up a bit...x = 3/2 + ln(2)/ln(25)
25^x=2505^(2x)=5^3•25^(2x-3)=2(2x-3)log5=log2x=(1/2)[3+(log2)/(log5)]
25^x = 250
Take the natural log of both sides...
x * ln(25) = ln(125 * 2)
x * ln(25) = ln(125) + ln (2)
x * 2ln(5) = 3ln(5) + ln(2)
Divide both sides by 2ln(5)
x = 3/2 + ln(2)/2ln(5)
Clean it up a bit...
x = 3/2 + ln(2)/ln(25)
25^x=250
5^(2x)=5^3•2
5^(2x-3)=2
(2x-3)log5=log2
x=(1/2)[3+(log2)/(log5)]