What is the value of 5sinh(2ln(4)) ?

The value of 5sinh(2ln(4)) is 1275/32

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Popular >

5sinh(2ln(4))

Solution

5 sinh (2 ln (4))

Solution

\frac{1275}{32}

Decimal Notation

39.84375

Solution steps

5 sinh (2 ln (4))

Simplify:

2 ln (4) = 4 ln (2)

2 ln (4)

Simplify

ln (4) : 2 ln (2)

ln (4)

Rewrite

4

in power-base form:

4 = 2^{2}

= ln (2^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (2^{2}) = 2 ln (2)

= 2 ln (2)

= 2 \cdot 2 ln (2)

Multiply the numbers:

2 \cdot 2 = 4

= 4 ln (2)

= 5 sinh (4 ln (2))

Rewrite using trig identities:

sinh (4 ln (2)) = \frac{255}{32}

sinh (4 ln (2))

Use the Hyperbolic identity:

sinh (x) = \frac{e ^{x} - e ^{- x}}{2}

= \frac{e ^{4 l n (2)} - e ^{- 4 l n (2)}}{2}

\frac{e ^{4 l n (2)} - e ^{- 4 l n (2)}}{2} = \frac{255}{32}

\frac{e ^{4 l n (2)} - e ^{- 4 l n (2)}}{2}

e^{4 l n (2)} = 2^{4}

e^{4 l n (2)}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

= (e^{l n (2)})^{4}

Apply log rule:

a^{l o g_{a} (b)} = b

e^{l n (2)} = 2

= 2^{4}

e^{- 4 l n (2)} = 2^{- 4}

e^{- 4 l n (2)}

Apply exponent rule:

a^{b c} = (a^{b})^{c}

= (e^{l n (2)})^{- 4}

Apply log rule:

a^{l o g_{a} (b)} = b

e^{l n (2)} = 2

= 2^{- 4}

= \frac{2 ^{4} - 2 ^{- 4}}{2}

Simplify

\frac{2 ^{4} - 2 ^{- 4}}{2}

2^{4} = 16

= \frac{16 - 2 ^{- 4}}{2}

2^{- 4} = \frac{1}{16}

2^{- 4}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{2 ^{4}}

2^{4} = 16

= \frac{1}{16}

= \frac{16 - \frac{1}{16}}{2}

Join

16 - \frac{1}{16} : \frac{255}{16}

16 - \frac{1}{16}

Convert element to fraction:

16 = \frac{16 \cdot 16}{16}

= \frac{16 \cdot 16}{16} - \frac{1}{16}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{16 \cdot 16 - 1}{16}

16 \cdot 16 - 1 = 255

16 \cdot 16 - 1

Multiply the numbers:

16 \cdot 16 = 256

= 256 - 1

Subtract the numbers:

256 - 1 = 255

= 255

= \frac{255}{16}

= \frac{\frac{255}{16}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{255}{16 \cdot 2}

Multiply the numbers:

16 \cdot 2 = 32

= \frac{255}{32}

= \frac{255}{32}

= \frac{255}{32}

= 5 \cdot \frac{255}{32}

5 \cdot \frac{255}{32} = \frac{1275}{32}

5 \cdot \frac{255}{32}

Convert element to fraction:

5 = \frac{5}{1}

= \frac{5}{1} \cdot \frac{255}{32}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{5 \cdot 255}{1 \cdot 32}

Multiply the numbers:

5 \cdot 255 = 1275

= \frac{1275}{1 \cdot 32}

Multiply the numbers:

1 \cdot 32 = 32

= \frac{1275}{32}

= \frac{1275}{32}

Popular Examples

sec(2(pi/4))

sec (2 (\frac{π}{4}))

(cos^2(pi))/3

\frac{cos ^{2} ( π )}{3}

2cos(3)((2pi)/3)

2 cos (3) (\frac{2 π}{3})

3sec^4(0)

3 sec^{4} (0)

3.25cos(pi/6*9)+19.15

3.25 cos (\frac{π}{6} \cdot 9) + 19.15

Frequently Asked Questions (FAQ)

What is the value of 5sinh(2ln(4)) ?
The value of 5sinh(2ln(4)) is 1275/32