×

# 75^40=9^20*5^x

can anyone tell me how to solve this.

Note by Daniel Kua
2 years, 2 months ago

Sort by:

X=80 · 2 years ago

x=80 · 2 years, 2 months ago

Which one do you mean I or II :

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

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

· 2 years, 2 months ago

the 2nd one · 2 years, 2 months ago

Sorry for the late response,

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

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

$$75^{40} = 3^{40} \times 5^{x}$$

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

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

$$25^{40} = 5^{x}$$

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

$$5^{80} = 5^{x}$$

$$\boxed{x = 80}$$ · 2 years, 2 months ago

$$75^{40}= (3*25)^{40}$$

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

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

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

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

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 · 2 years, 2 months ago

3^40 is not equal to 3^20+2 · 2 years, 2 months ago

Its $$3^{20 \times 2}$$. I used the $$*$$ symbol. · 2 years, 2 months ago

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? · 2 years, 2 months ago

how do u type multiple again? tell me pls. · 2 years, 2 months ago

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. · 2 years, 2 months ago