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

The answer to 3^x=10-(log_{10}(x))/(log_{2)(x)} is x=(ln(10-log_{10}(2)))/(ln(3))

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

The solution is x=(ln(10-log_{10}(2)))/(ln(3))

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

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

Decimal Notation

x = 2.06808 \dots

Solution steps

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

Multiply both sides by

lo g_{2} (x)

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

Simplify

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

Apply log rules

lo g_{10} (x) (3^{x} - 10 + lo g_{10} (2)) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

lo g_{10} (x) = 0 or 3^{x} - 10 + lo g_{10} (2) = 0

Solve

lo g_{10} (x) = 0 : x = 1

Solve

3^{x} - 10 + lo g_{10} (2) = 0 : x = \frac{ln ( 10 - lo g _{10} ( 2 ) )}{ln ( 3 )}

Verify Solutions:

x = 1

False

, x = \frac{ln ( 10 - lo g _{10} ( 2 ) )}{ln ( 3 )}

True

The solution is

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

x, lo g_{3} (x) + lo g_{3} (y) = 0

lo g_{5} (14 x + 5) = 9

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

m, \frac{1}{2} \cdot lo g_{3} (m) + 3 lo g_{3} (n) = 1

lo g_{5} (x) - lo g_{5} (2 x - 1) - lo g_{10} (625) = 0

What is the answer to 3^x=10-(log_{10}(x))/(log_{2)(x)} ?
The answer to 3^x=10-(log_{10}(x))/(log_{2)(x)} is x=(ln(10-log_{10}(2)))/(ln(3))
Solve for x: 3^x=10-(log_{10}(x))/(log_{2)(x)}
The solution is x=(ln(10-log_{10}(2)))/(ln(3))