What is the answer to 16log_{r}(4)=log_{4}(r) ?

The answer to 16log_{r}(4)=log_{4}(r) is r=256,r= 1/256

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16log_{r}(4)=log_{4}(r)

16 lo g_{r} (4) = lo g_{4} (r)

r = 256, r = \frac{1}{256}

Decimal Notation

r = 256, r = 0.00390625

Solution steps

16 lo g_{r} (4) = lo g_{4} (r)

Apply log rules

\frac{16}{lo g _{4} ( r )} = lo g_{4} (r)

Rewrite the equation with

lo g_{4} (r) = u

\frac{16}{u} = u

Solve

\frac{16}{u} = u : u = 4, u = - 4

u = 4, u = - 4

Substitute back

u = lo g_{4} (r),

solve for

r

Solve

lo g_{4} (r) = 4 : r = 256

Solve

lo g_{4} (r) = - 4 : r = \frac{1}{256}

r = 256, r = \frac{1}{256}

Verify Solutions:

r = 256

True

, r = \frac{1}{256}

True

The solutions are

r = 256, r = \frac{1}{256}

lo g_{3} (x^{2} - 3 x + 1) = 0

lo g_{10} (x) = 0.61

lo g_{10} (8) = 3 - 3 lo g_{10} (x)

0.891 = ln (x^{3})

x, ln (y) = 4 ln (x) + c

What is the answer to 16log_{r}(4)=log_{4}(r) ?
The answer to 16log_{r}(4)=log_{4}(r) is r=256,r= 1/256
Solve for r: 16log_{r}(4)=log_{4}(r)
The solution is r=256,r= 1/256