75^40=9^20*5^x

can anyone tell me how to solve this.

#Algebra #AlgebraicExponents

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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 - 6 years, 4 months ago

no.2

Daniel Kua - 6 years, 4 months ago

how do u type multiple again? tell me pls.

Daniel Kua - 6 years, 4 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.

Andronikus Lumembang - 6 years, 4 months ago

the 2nd one

Daniel Kua - 6 years, 4 months ago

Sorry for the late response,

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

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

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

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

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

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

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

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

$\boxed{x = 80}$

Andronikus Lumembang - 6 years, 4 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

Siddhartha Srivastava - 6 years, 4 months ago

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

Daniel Kua - 6 years, 4 months ago

@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 - 6 years, 4 months ago

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

Siddhartha Srivastava - 6 years, 4 months ago

x=80

Zalza Puspita - 6 years, 4 months ago

X=80

Aditya Chauhan - 6 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$