What is the answer to log_{m}(4)+8log_{4}(m)=6 ?

The answer to log_{m}(4)+8log_{4}(m)=6 is m=2,m=sqrt(2)

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log_{m}(4)+8log_{4}(m)=6

lo g_{m} (4) + 8 lo g_{4} (m) = 6

m = 2, m = 2

Decimal Notation

m = 2, m = 1.41421 \dots

Solution steps

lo g_{m} (4) + 8 lo g_{4} (m) = 6

Apply log rules

\frac{1}{lo g _{4} ( m )} + 8 lo g_{4} (m) = 6

Rewrite the equation with

lo g_{4} (m) = u

\frac{1}{u} + 8 u = 6

Solve

\frac{1}{u} + 8 u = 6 : u = \frac{1}{2}, u = \frac{1}{4}

u = \frac{1}{2}, u = \frac{1}{4}

Substitute back

u = lo g_{4} (m),

solve for

m

Solve

lo g_{4} (m) = \frac{1}{2} : m = 2

Solve

lo g_{4} (m) = \frac{1}{4} : m = 2

m = 2, m = 2

Verify Solutions:

m = 2

True

, m = 2

True

The solutions are

m = 2, m = 2

ln (x + 2) - ln (x + 1) = 0

1 0^{6} = lo g_{2} (x)

lo g_{10} (a) = 3.931

2 ln (x) - ln (x) = ln (4)

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

What is the answer to log_{m}(4)+8log_{4}(m)=6 ?
The answer to log_{m}(4)+8log_{4}(m)=6 is m=2,m=sqrt(2)
Solve for m: log_{m}(4)+8log_{4}(m)=6
The solution is m=2,m=sqrt(2)