75^40=9^20*5^x

can anyone tell me how to solve this.

Note by Daniel Kua
4 years, 6 months ago

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Which one do you mean I or II :

  • 7540=920×5x.....I75^{40} = 9^{20 \times 5^{x}} . . . . . I

  • 7540=920×5x.....II 75^{40} = 9^{20} \times 5^{x} . . . . .II

Andronikus Lumembang - 4 years, 6 months ago

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no.2

Daniel Kua - 4 years, 6 months ago

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how do u type multiple again? tell me pls.

Daniel Kua - 4 years, 6 months ago

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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 - 4 years, 6 months ago

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the 2nd one

Daniel Kua - 4 years, 6 months ago

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Sorry for the late response,

7540=920×5x75^{40} = 9^{20} \times 5^{x}

7540=(32)20×5x75^{40} = (3^2)^{20} \times 5^{x}

7540=340×5x75^{40} = 3^{40} \times 5^{x}

7540340=5x\frac{75^{40}}{3^{40}} = 5^{x}

(753)40=5x(\frac{75}{3})^{40} = 5^{x}

2540=5x25^{40} = 5^{x}

(52)40=5x(5^2)^{40} = 5^{x}

580=5x5^{80} = 5^{x}

x=80\boxed{x = 80}

Andronikus Lumembang - 4 years, 6 months ago

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7540=(325)40 75^{40}= (3*25)^{40}

=3402540 = 3^{40} * 25^{40}

=3220(52)40 = 3^{2*20} * (5^2)^{40}

=(32)205240 = (3^2)^{20} * 5^{2*40}

=920580 = 9^{20}*5^{80}

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

Also, to write all the signs, read this

Siddhartha Srivastava - 4 years, 6 months ago

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@Siddhartha Srivastava 3^40 is not equal to 3^20+2

Daniel Kua - 4 years, 5 months ago

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

ax×ay=ax+y a^x \times a^y = a^{x+y}

(ax)y=axy(a^x)^y = a^{xy}

So,

340320+23^{40} \neq 3^{20+2} but

340=32×20=(32)203^{40} = 3^{2 \times 20} = (3^2)^{20}

Got it?

Andronikus Lumembang - 4 years, 5 months ago

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@Daniel Kua Its 320×2 3^{20 \times 2} . I used the * symbol.

Siddhartha Srivastava - 4 years, 5 months ago

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x=80

Zalza Puspita - 4 years, 5 months ago

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X=80

Aditya Chauhan - 4 years, 3 months ago

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