What is the answer to ((2+log_{10}(x)))/((3-log_{10)(x))}=5 ?

The answer to ((2+log_{10}(x)))/((3-log_{10)(x))}=5 is x=100\sqrt[6]{10}

Solve for x: ((2+log_{10}(x)))/((3-log_{10)(x))}=5

The solution is x=100\sqrt[6]{10}

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\frac{( 2 + lo g _{10} ( x ) )}{( 3 - lo g _{10} ( x ) )} = 5

Decimal Notation

x = 146.77992 \dots

Solution steps

\frac{( 2 + lo g _{10} ( x ) )}{( 3 - lo g _{10} ( x ) )} = 5

Multiply both sides by

3 - lo g_{10} (x)

\frac{2 + lo g _{10} ( x )}{3 - lo g _{10} ( x )} (3 - lo g_{10} (x)) = 5 (3 - lo g_{10} (x))

Simplify

2 + lo g_{10} (x) = 5 (3 - lo g_{10} (x))

Expand

5 (3 - lo g_{10} (x)) : 15 - 5 lo g_{10} (x)

2 + lo g_{10} (x) = 15 - 5 lo g_{10} (x)

Move

2

to the right side

lo g_{10} (x) = - 5 lo g_{10} (x) + 13

Move

5 lo g_{10} (x)

to the left side

6 lo g_{10} (x) = 13

Divide both sides by

6

lo g_{10} (x) = \frac{13}{6}

Apply log rules

Verify Solutions:

True

The solution is

lo g_{10} (1 - 2 x) = 1

ln (\frac{( x + 6 )}{( x + 2 )}) = ln (x)

lo g_{3} (x) = 1.4

lo g_{2} (x^{2} - 25) - lo g_{2} (x - 5) = 4

lo g_{4} (5 p - 6) = lo g_{4} (4 p + 2)

What is the answer to ((2+log_{10}(x)))/((3-log_{10)(x))}=5 ?
The answer to ((2+log_{10}(x)))/((3-log_{10)(x))}=5 is x=100\sqrt[6]{10}
Solve for x: ((2+log_{10}(x)))/((3-log_{10)(x))}=5
The solution is x=100\sqrt[6]{10}