Practice makes perfect. The simplification to y is tricky. I would need to practice this through more examples. The clue is to know the laws of indices, exponents and logarithms and when and how to use them. Thank-you for this example which was/is challenging.
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My take. Divide the given equation by 10^x: (4/10)^x-7+10(25/10)^x=(2/5)^x-7+10/(2/5)^x=0. Substitute y=(2/5)^x: y-7+10/y=0. Multiply by y: y^2-7y+10=0. Solve for y: y=(7±3)/2=5 or 2. Solve for x: x=ln2/ln(2/5) or x=ln5/ln(2/5)
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@@MercyCosmas-z3b
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@@titustarhemba4678
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@@aravindhnagarathinam
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Practice makes perfect. The simplification to y is tricky. I would need to practice this through more examples. The clue is to know the laws of indices, exponents and logarithms and when and how to use them. Thank-you for this example which was/is challenging.
@@tomquail6959
Amazing and thank you for engaging. We promise to expose more Tips 🙏🏆🏆🏆🏆
Your knowledge in maths is deep.
How can I possess this kind of knowledge ma?
@@VictorOyekwu
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Practice and Determination okay 🙏👍
For further studies on #matholympiad exponential equations, kindly click the link th-cam.com/play/PLVcWSTbc_4a2v3prPWnDhJSi--js_DBbw.html&si=IdxDGSSOIAKAKJyx
My take. Divide the given equation by 10^x: (4/10)^x-7+10(25/10)^x=(2/5)^x-7+10/(2/5)^x=0.
Substitute y=(2/5)^x: y-7+10/y=0. Multiply by y: y^2-7y+10=0. Solve for y: y=(7±3)/2=5 or 2.
Solve for x: x=ln2/ln(2/5) or x=ln5/ln(2/5)
@@wes9627
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@@GodonUm
Smiles ! Thanks a lot 🙏