What is the answer to log_{x}(64)+3*log_{4}(x)-log_{x}(4)=5 ?

The answer to log_{x}(64)+3*log_{4}(x)-log_{x}(4)=5 is x=4,x=4^{2/3}

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log_{x}(64)+3*log_{4}(x)-log_{x}(4)=5

lo g_{x} (64) + 3 \cdot lo g_{4} (x) - lo g_{x} (4) = 5

x = 4, x = 4^{\frac{2}{3}}

Decimal Notation

x = 4, x = 2.51984 \dots

Solution steps

lo g_{x} (64) + 3 lo g_{4} (x) - lo g_{x} (4) = 5

Apply log rules

\frac{2}{lo g _{4} ( x )} + 3 lo g_{4} (x) = 5

Rewrite the equation with

lo g_{4} (x) = u

\frac{2}{u} + 3 u = 5

Solve

\frac{2}{u} + 3 u = 5 : u = 1, u = \frac{2}{3}

u = 1, u = \frac{2}{3}

Substitute back

u = lo g_{4} (x),

solve for

x

Solve

lo g_{4} (x) = 1 : x = 4

Solve

lo g_{4} (x) = \frac{2}{3} : x = 4^{\frac{2}{3}}

x = 4, x = 4^{\frac{2}{3}}

Verify Solutions:

x = 4

True

, x = 4^{\frac{2}{3}}

True

The solutions are

x = 4, x = 4^{\frac{2}{3}}

lo g_{27} (x) = 3

\frac{1}{2 lo g _{10} ( 7 x - 3 )} = - 5

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

lo g_{5} (x^{3}) + 13 x - 5 = 0

lo g_{2} (x - 1) + x = 1

What is the answer to log_{x}(64)+3*log_{4}(x)-log_{x}(4)=5 ?
The answer to log_{x}(64)+3*log_{4}(x)-log_{x}(4)=5 is x=4,x=4^{2/3}
Solve for x: log_{x}(64)+3*log_{4}(x)-log_{x}(4)=5
The solution is x=4,x=4^{2/3}