What is the answer to 1/(3-log_{10)(x)}+1/(1+log_{10)(x)}=1 ?

The answer to 1/(3-log_{10)(x)}+1/(1+log_{10)(x)}=1 is x=10

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1/(3-log_{10)(x)}+1/(1+log_{10)(x)}=1

\frac{1}{3 - lo g _{10} ( x )} + \frac{1}{1 + lo g _{10} ( x )} = 1

x = 10

Solution steps

\frac{1}{3 - lo g _{10} ( x )} + \frac{1}{1 + lo g _{10} ( x )} = 1

Find Least Common Multiplier of

3 - lo g_{10} (x), 1 + lo g_{10} (x) : (- lo g_{10} (x) + 3) (lo g_{10} (x) + 1)

Multiply by LCM=

(- lo g_{10} (x) + 3) (lo g_{10} (x) + 1)

\frac{1}{3 - lo g _{10} ( x )} (- lo g_{10} (x) + 3) (lo g_{10} (x) + 1) + \frac{1}{1 + lo g _{10} ( x )} (- lo g_{10} (x) + 3) (lo g_{10} (x) + 1) = 1 \cdot (- lo g_{10} (x) + 3) (lo g_{10} (x) + 1)

Simplify

4 = (- lo g_{10} (x) + 3) (lo g_{10} (x) + 1)

Rewrite the equation with

lo g_{10} (x) = u

4 = (- u + 3) (u + 1)

Solve

4 = (- u + 3) (u + 1) : u = 1

u = 1

Substitute back

u = lo g_{10} (x),

solve for

x

Solve

lo g_{10} (x) = 1 : x = 10

x = 10

Verify Solutions:

x = 10

True

The solution is

x = 10

lo g_{10} (w - 12) = 4.9

lo g_{6} (x + 4) + lo g_{6} (x - 2) = lo g_{6} (4 x)

lo g_{10} (x) = - 2.2

(lo g_{5} (x))^{2} + 5 lo g_{5} (x) + 6 = 0

0.001 = \frac{ln ( x )}{x}

What is the answer to 1/(3-log_{10)(x)}+1/(1+log_{10)(x)}=1 ?
The answer to 1/(3-log_{10)(x)}+1/(1+log_{10)(x)}=1 is x=10
Solve for x: 1/(3-log_{10)(x)}+1/(1+log_{10)(x)}=1
The solution is x=10