What is the answer to log_{b}(7)-2log_{7}(b)+1=0 ?

The answer to log_{b}(7)-2log_{7}(b)+1=0 is b= 1/(sqrt(7)),b=7

Solve for b: log_{b}(7)-2log_{7}(b)+1=0

The solution is b= 1/(sqrt(7)),b=7

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lo g_{b} (7) - 2 lo g_{7} (b) + 1 = 0

b = \frac{1}{7}, b = 7

Decimal Notation

b = 0.37796 \dots, b = 7

Solution steps

lo g_{b} (7) - 2 lo g_{7} (b) + 1 = 0

Apply log rules

\frac{1}{lo g _{7} ( b )} - 2 lo g_{7} (b) + 1 = 0

Rewrite the equation with

lo g_{7} (b) = u

\frac{1}{u} - 2 u + 1 = 0

Solve

\frac{1}{u} - 2 u + 1 = 0 : u = - \frac{1}{2}, u = 1

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

Substitute back

u = lo g_{7} (b),

solve for

b

Solve

lo g_{7} (b) = - \frac{1}{2} : b = \frac{1}{7}

Solve

lo g_{7} (b) = 1 : b = 7

b = \frac{1}{7}, b = 7

Verify Solutions:

b = \frac{1}{7}

True

, b = 7

True

The solutions are

b = \frac{1}{7}, b = 7

ln (x) + ln (x + 4) = 3

0.67 = ln (y)

ln (3 x) + ln (2 x) = 9

ln (e) + 4 ln (x) = ln (e^{5})

lo g_{10} (x) = 6.6

What is the answer to log_{b}(7)-2log_{7}(b)+1=0 ?
The answer to log_{b}(7)-2log_{7}(b)+1=0 is b= 1/(sqrt(7)),b=7
Solve for b: log_{b}(7)-2log_{7}(b)+1=0
The solution is b= 1/(sqrt(7)),b=7