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Divide x^{3}-125 by x-5 to get x^{2}+5x+25. Solve the equation where the result equals to 0. x=\frac{-5±\sqrt{5^{2}-4\times 1\times 25}}{2} All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, 5 for b, and 25 for c in the quadratic formula.
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Detailed step by step solution for 125^x=25
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Precalculus. Solve for x 125=25^ (x-1) 125 = 25x−1 125 = 25 x - 1. Rewrite the equation as 25x−1 = 125 25 x - 1 = 125. 25x−1 = 125 25 x - 1 = 125. Create equivalent expressions in the equation that all have equal bases. 52(x−1) = 53 5 2 ( x - 1) = 5 3. Since the bases are the same, then two expressions are only equal if the exponents.
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125x=25125 to the power of x equals 25Take the log of both sides log10(125x)=log10(25) Rewrite the left side of the equation using the rule for the log of a power x•log10(125)=log10(25) Isolate.
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Trigonometry. Solve for x 25^x=1/125. 25x = 1 125 25 x = 1 125. Raise 125 125 to the power of 1 1. 25x = 1 1251 25 x = 1 125 1. Move 1251 125 1 to the numerator using the negative exponent rule 1 bn = b−n 1 b n = b - n. 25x = 125−1 25 x = 125 - 1. Create equivalent expressions in the equation that all have equal bases. 52x = 5−3 5 2 x = 5.
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x=log_125(25) Decimal form: x = 0.6666666666666666. x=0.6666666666666666. See steps. Other Ways to Solve. Exponential equations using logarithms. Step-by-step explanation. 1. Remove the variable from the exponent using logarithms. 125 x = 25. Take the common logarithm of both sides of the equation:
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Solve for x 125^x=25. 125x = 25 125 x = 25. Create equivalent expressions in the equation that all have equal bases. 53x = 52 5 3 x = 5 2. Since the bases are the same, then two expressions are only equal if the exponents are also equal. 3x = 2 3 x = 2. Divide each term in 3x = 2 3 x = 2 by 3 3 and simplify.
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Method 1- Common base I noticed that both 25 and 125 are 5 to some power. So therefore I can safely state that: #5^(2x)= 1/5^3# #5^(2x)= 5^(-3)# Now that we have a common base of 5, I can just set the exponents equal to one another.
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