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75^40=9^20*5^x

can anyone tell me how to solve this.

Note by Daniel Kua
2 years, 2 months ago

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X=80 Aditya Chauhan · 2 years ago

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x=80 Zalza Puspita · 2 years, 2 months ago

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Which one do you mean I or II :

  • \(75^{40} = 9^{20 \times 5^{x}} . . . . . I \)

  • \( 75^{40} = 9^{20} \times 5^{x} . . . . .II \)

Andronikus Lumembang · 2 years, 2 months ago

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@Andronikus Lumembang the 2nd one Daniel Kua · 2 years, 2 months ago

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@Daniel Kua Sorry for the late response,

\(75^{40} = 9^{20} \times 5^{x}\)

\(75^{40} = (3^2)^{20} \times 5^{x}\)

\(75^{40} = 3^{40} \times 5^{x}\)

\(\frac{75^{40}}{3^{40}} = 5^{x}\)

\((\frac{75}{3})^{40} = 5^{x}\)

\(25^{40} = 5^{x}\)

\((5^2)^{40} = 5^{x}\)

\(5^{80} = 5^{x}\)

\(\boxed{x = 80}\) Andronikus Lumembang · 2 years, 2 months ago

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@Daniel Kua \( 75^{40}= (3*25)^{40} \)

\( = 3^{40} * 25^{40} \)

\( = 3^{2*20} * (5^2)^{40} \)

\( = (3^2)^{20} * 5^{2*40} \)

\( = 9^{20}*5^{80} \)

Therefore \( x = 80 \). I only used 2 formulae, \( (ab)^n = a^n * b^n \) and \( (a^n)^m = a^{m*n} \)

Also, to write all the signs, read this Siddhartha Srivastava · 2 years, 2 months ago

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@Siddhartha Srivastava 3^40 is not equal to 3^20+2 Daniel Kua · 2 years, 2 months ago

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@Daniel Kua Its \( 3^{20 \times 2} \). I used the \( * \) symbol. Siddhartha Srivastava · 2 years, 2 months ago

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@Daniel Kua Of course not. Look at this exponent's formulas :

\( a^x \times a^y = a^{x+y}\)

\((a^x)^y = a^{xy}\)

So,

\(3^{40} \neq 3^{20+2}\) but

\(3^{40} = 3^{2 \times 20} = (3^2)^{20}\)

Got it? Andronikus Lumembang · 2 years, 2 months ago

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@Andronikus Lumembang how do u type multiple again? tell me pls. Daniel Kua · 2 years, 2 months ago

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@Daniel Kua You can see how to type in math formatting by click on "formatting guide" at the bottom-left corner of your comment box.

To type multiple, just type " \times " in math format (remember, in math format! See how to start a math format in the formatting guide.

The more easy ways to know the format of symbols, just point your cursor at the symbols, the format then will appears. Andronikus Lumembang · 2 years, 2 months ago

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@Andronikus Lumembang no.2 Daniel Kua · 2 years, 2 months ago

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