What is the answer to |3^x+4|=|3^x-9| ?

The answer to |3^x+4|=|3^x-9| is x=(ln(5/2))/(ln(3))

Solve for x: |3^x+4|=|3^x-9|

The solution is x=(ln(5/2))/(ln(3))

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∣ 3^{x} + 4 ∣ = ∣ 3^{x} - 9 ∣

x = \frac{ln ( \frac{5}{2} )}{ln ( 3 )}

Decimal Notation

x = 0.83404 \dots

Solution steps

∣ 3^{x} + 4 ∣ = ∣ 3^{x} - 9 ∣

Rewrite the equation with

3^{x} = u

∣ u + 4 ∣ = ∣ u - 9 ∣

Solve

∣ u + 4 ∣ = ∣ u - 9 ∣ : u = \frac{5}{2}

u = \frac{5}{2}

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = \frac{5}{2} : x = \frac{ln ( \frac{5}{2} )}{ln ( 3 )}

x = \frac{ln ( \frac{5}{2} )}{ln ( 3 )}

(103)^{2}

13.1 x + 23.1 < - 16.2

40 \div 4 - (5 - 3)

m^{2} - 11 m + 30

6 x + 18 y

What is the answer to |3^x+4|=|3^x-9| ?
The answer to |3^x+4|=|3^x-9| is x=(ln(5/2))/(ln(3))
Solve for x: |3^x+4|=|3^x-9|
The solution is x=(ln(5/2))/(ln(3))