What is the answer to 2700=2^m*3^n*5^p ?

The answer to 2700=2^m*3^n*5^p is p=(2ln(5)+ln(3)(-n+3)+ln(2)(-m+2))/(ln(5))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2700=2^m3^n5^p

2700 = 2^{m} \cdot 3^{n} \cdot 5^{p}

p = \frac{2 ln ( 5 ) + ln ( 3 ) ( - n + 3 ) + ln ( 2 ) ( - m + 2 )}{ln ( 5 )}

Solution steps

2700 = 2^{m} \cdot 3^{n} \cdot 5^{p}

Switch sides

2^{m} \cdot 3^{n} \cdot 5^{p} = 2700

Divide both sides by

2^{m} \cdot 3^{n}

5^{p} = \frac{2700}{2 ^{m} \cdot 3 ^{n}}

Simplify

\frac{2700}{2 ^{m} \cdot 3 ^{n}} : 25 \cdot 2^{2 - m} \cdot 3^{3 - n}

5^{p} = 25 \cdot 2^{2 - m} \cdot 3^{3 - n}

Apply exponent rules

p ln (5) = ln (25 \cdot 2^{2 - m} \cdot 3^{3 - n})

Solve

p ln (5) = ln (25 \cdot 2^{2 - m} \cdot 3^{3 - n}) : p = \frac{2 ln ( 5 ) + ln ( 3 ) ( - n + 3 ) + ln ( 2 ) ( - m + 2 )}{ln ( 5 )}

p = \frac{2 ln ( 5 ) + ln ( 3 ) ( - n + 3 ) + ln ( 2 ) ( - m + 2 )}{ln ( 5 )}

2^{x + 5} + 2^{x + 4} + 2^{x + 3} = 112

y, (1 + x)^{y} = \frac{1}{( 1 - x )}

x, q^{x} + 1 = 3

(a) 1.2 \cdot 1 0^{6} = 12 \cdot 1 0^{x}, x

\frac{( 2 ^{n + 1} + 2 ^{n} )}{( 2 ^{n + 4} - 2 ^{n - 1} )} = 1

What is the answer to 2700=2^m*3^n*5^p ?
The answer to 2700=2^m*3^n*5^p is p=(2ln(5)+ln(3)(-n+3)+ln(2)(-m+2))/(ln(5))