Solve 16*5^(1-8/x)-189*20

Question

Simplify the expression

16 \times 5^{\frac{x - 8}{x}} - 3780

Show Solution

20 (4 \times 5^{- \frac{8}{x}} - 189)

Show Solution

x = \frac{8}{- lo g _{5} ( 189 ) + 2 lo g _{5} ( 2 )}

Alternative Form

x \approx - 3.339557

Evaluate

16 \times 5^{1 - \frac{8}{x}} - 189 \times 20

To find the roots of the expression,set the expression equal to 0

16 \times 5^{1 - \frac{8}{x}} - 189 \times 20 = 0

Find the domain

16 \times 5^{1 - \frac{8}{x}} - 189 \times 20 = 0, x \neq = 0

Calculate

16 \times 5^{1 - \frac{8}{x}} - 189 \times 20 = 0

Subtract the terms

More Steps

16 \times 5^{\frac{x - 8}{x}} - 189 \times 20 = 0

Multiply the numbers

16 \times 5^{\frac{x - 8}{x}} - 3780 = 0

Rewrite the expression

16 \times 5^{\frac{x - 8}{x}} = 3780

Divide both sides

\frac{16 \times 5 ^{\frac{x - 8}{x}}}{16} = \frac{3780}{16}

Divide the numbers

5^{\frac{x - 8}{x}} = \frac{3780}{16}

Cancel out the common factor 4

5^{\frac{x - 8}{x}} = \frac{945}{4}

Take the logarithm of both sides

lo g_{5} (5^{\frac{x - 8}{x}}) = lo g_{5} (\frac{945}{4})

Evaluate the logarithm

\frac{x - 8}{x} = lo g_{5} (\frac{945}{4})

Cross multiply

x - 8 = x lo g_{5} (\frac{945}{4})

Simplify the equation

x - 8 = lo g_{5} (\frac{945}{4}) \times x

Move the variable to the left side

x - 8 - lo g_{5} (\frac{945}{4}) \times x = 0

Collect like terms by calculating the sum or difference of their coefficients

(1 - lo g_{5} (\frac{945}{4})) x - 8 = 0

Move the constant to the right side

(1 - lo g_{5} (\frac{945}{4})) x = 0 + 8

Removing 0 doesn't change the value,so remove it from the expression

(1 - lo g_{5} (\frac{945}{4})) x = 8

Divide both sides

\frac{( 1 - lo g _{5} ( \frac{945}{4} ) ) x}{1 - lo g _{5} ( \frac{945}{4} )} = \frac{8}{1 - lo g _{5} ( \frac{945}{4} )}

Divide the numbers

x = \frac{8}{1 - lo g _{5} ( \frac{945}{4} )}

Simplify

More Steps

x = \frac{8}{- lo g _{5} ( 189 ) + 2 lo g _{5} ( 2 )}

Check if the solution is in the defined range

x = \frac{8}{- lo g _{5} ( 189 ) + 2 lo g _{5} ( 2 )}, x \neq = 0

Solution

x = \frac{8}{- lo g _{5} ( 189 ) + 2 lo g _{5} ( 2 )}

Alternative Form

x \approx - 3.339557

Show Solution