What is the answer to log_{7}(x)=9log_{x}(7) ?

The answer to log_{7}(x)=9log_{x}(7) is x=343,x= 1/343

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log_{7}(x)=9log_{x}(7)

lo g_{7} (x) = 9 lo g_{x} (7)

x = 343, x = \frac{1}{343}

Decimal Notation

x = 343, x = 0.00291 \dots

Solution steps

lo g_{7} (x) = 9 lo g_{x} (7)

Apply log rules

lo g_{7} (x) = \frac{9}{lo g _{7} ( x )}

Rewrite the equation with

lo g_{7} (x) = u

u = \frac{9}{u}

Solve

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

u = 3, u = - 3

Substitute back

u = lo g_{7} (x),

solve for

x

Solve

lo g_{7} (x) = 3 : x = 343

Solve

lo g_{7} (x) = - 3 : x = \frac{1}{343}

x = 343, x = \frac{1}{343}

Verify Solutions:

x = 343

True

, x = \frac{1}{343}

True

The solutions are

x = 343, x = \frac{1}{343}

lo g_{10} (x^{2} + 2 x - 8) = 0

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

- ln (2 + x) = 2

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

y, ln (y) = 0

What is the answer to log_{7}(x)=9log_{x}(7) ?
The answer to log_{7}(x)=9log_{x}(7) is x=343,x= 1/343
Solve for x: log_{7}(x)=9log_{x}(7)
The solution is x=343,x= 1/343