What is the answer to 9log_{5}(x)=25log_{x}(5) ?

The answer to 9log_{5}(x)=25log_{x}(5) is x=5*5^{2/3},x= 1/(5*5^{2/3)}

Solve for x: 9log_{5}(x)=25log_{x}(5)

The solution is x=5*5^{2/3},x= 1/(5*5^{2/3)}

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9 lo g_{5} (x) = 25 lo g_{x} (5)

x = 5 \cdot 5^{\frac{2}{3}}, x = \frac{1}{5 \cdot 5 ^{\frac{2}{3}}}

Decimal Notation

x = 14.62008 \dots, x = 0.06839 \dots

Solution steps

9 lo g_{5} (x) = 25 lo g_{x} (5)

Apply log rules

9 lo g_{5} (x) = \frac{25}{lo g _{5} ( x )}

Rewrite the equation with

lo g_{5} (x) = u

9 u = \frac{25}{u}

Solve

9 u = \frac{25}{u} : u = \frac{5}{3}, u = - \frac{5}{3}

u = \frac{5}{3}, u = - \frac{5}{3}

Substitute back

u = lo g_{5} (x),

solve for

x

Solve

lo g_{5} (x) = \frac{5}{3} : x = 5 \cdot 5^{\frac{2}{3}}

Solve

lo g_{5} (x) = - \frac{5}{3} : x = \frac{1}{5 \cdot 5 ^{\frac{2}{3}}}

x = 5 \cdot 5^{\frac{2}{3}}, x = \frac{1}{5 \cdot 5 ^{\frac{2}{3}}}

Verify Solutions:

x = 5 \cdot 5^{\frac{2}{3}}

True

, x = \frac{1}{5 \cdot 5 ^{\frac{2}{3}}}

True

The solutions are

x = 5 \cdot 5^{\frac{2}{3}}, x = \frac{1}{5 \cdot 5 ^{\frac{2}{3}}}

y, ln (y - 2) = x^{2} + 2

4 ln (6 x - 2) + 5 = 13

lo g_{5} (x^{3}) - 6 = 0

ln (3 + x) + ln (1 + x) = 3 ln (2)

- 19.7 = 20 lo g_{10} (\frac{1}{x})

What is the answer to 9log_{5}(x)=25log_{x}(5) ?
The answer to 9log_{5}(x)=25log_{x}(5) is x=5*5^{2/3},x= 1/(5*5^{2/3)}
Solve for x: 9log_{5}(x)=25log_{x}(5)
The solution is x=5*5^{2/3},x= 1/(5*5^{2/3)}