What is the answer to 2log_{m}(8)+3log_{8}(m)=7 ?

The answer to 2log_{m}(8)+3log_{8}(m)=7 is m=64,m=2

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2log_{m}(8)+3log_{8}(m)=7

2 lo g_{m} (8) + 3 lo g_{8} (m) = 7

m = 64, m = 2

Solution steps

2 lo g_{m} (8) + 3 lo g_{8} (m) = 7

Apply log rules

\frac{2}{lo g _{8} ( m )} + 3 lo g_{8} (m) = 7

Rewrite the equation with

lo g_{8} (m) = u

\frac{2}{u} + 3 u = 7

Solve

\frac{2}{u} + 3 u = 7 : u = 2, u = \frac{1}{3}

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

Substitute back

u = lo g_{8} (m),

solve for

m

Solve

lo g_{8} (m) = 2 : m = 64

Solve

lo g_{8} (m) = \frac{1}{3} : m = 2

m = 64, m = 2

Verify Solutions:

m = 64

True

, m = 2

True

The solutions are

m = 64, m = 2

y, ln (y) = 1

ln (x + 3) + ln (x - 1) = ln (4 x + 12)

lo g_{10} (x) = 5.833

lo g_{3} (x + 2) + lo g_{3} (x + 5) = 1

lo g_{4} (x + 2) = lo g_{4} (8)

What is the answer to 2log_{m}(8)+3log_{8}(m)=7 ?
The answer to 2log_{m}(8)+3log_{8}(m)=7 is m=64,m=2
Solve for m: 2log_{m}(8)+3log_{8}(m)=7
The solution is m=64,m=2