What is the answer to log_{x+1}(8)=2 ?

The answer to log_{x+1}(8)=2 is x=2sqrt(2)-1

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log_{x+1}(8)=2

lo g_{x + 1} (8) = 2

x = 22 - 1

Decimal

x = 1.82842 \dots

Solution steps

lo g_{x + 1} (8) = 2

Apply log rules

\frac{1}{lo g _{8} ( x + 1 )} = 2

Multiply both sides by

lo g_{8} (x + 1)

\frac{1}{lo g _{8} ( x + 1 )} lo g_{8} (x + 1) = 2 lo g_{8} (x + 1)

Simplify

1 = 2 lo g_{8} (x + 1)

Switch sides

2 lo g_{8} (x + 1) = 1

Divide both sides by

2

lo g_{8} (x + 1) = \frac{1}{2}

Apply log rules

x + 1 = 22

Solve

x + 1 = 22 : x = 22 - 1

x = 22 - 1

Verify Solutions:

x = 22 - 1

True

The solution is

x = 22 - 1

(ln (x))^{2} = 2 ln (x) + 3

lo g_{6} (y) = 3

lo g_{10} (2 x) = 4

ln (10 x) + 1 = 0

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

What is the answer to log_{x+1}(8)=2 ?
The answer to log_{x+1}(8)=2 is x=2sqrt(2)-1
Solve for x: log_{x+1}(8)=2
The solution is x=2sqrt(2)-1