Waste less time on Facebook — follow Brilliant.
×

Exponentiation Problem

Can anyone please help me in solving this problem?

\(60^{a} = 3\)

\(60^{b} = 5\)

\(12^{\frac{1 - a - b}{2(1 - b)}} = ?\)

I am just unable to solve it. So, any help would be highly appreciated.

Thanks.

Note by Nilabha Saha
1 year, 7 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. 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"
MathAppears 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

Sort by:

Top Newest

\(a=\dfrac{\log3}{\log{60}}\). \(b=\dfrac{\log5}{\log{60}}\).

\(12^{\frac{1-(a+b)}{2(1-b)}}\)\(=12^{\frac{1-\log15/\log{60}}{2(1-\log5/{60})}}=\)\(12^{\frac{\log4/\log{60}}{2(\log{12}/\log{60})}}=\)\(12^{\log2/\log{12}}=12^{\log_{12}{2}}=2\).

Note:

\(\log a+\log b=\log{ab}\)

\(\log a-\log b=\log{a/b}\)

\(\log a^2=2 \log a\)

\(a^{\log_a b}=b\).

Here, we take \(1=\log{60}/\log{60}\).

Brilliant Member - 1 year, 7 months ago

Log in to reply

Thank you very much.☺ Helped me understand a lot.😃😃😃

Nilabha Saha - 1 year, 7 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...