What is the answer to (4^{x-1})/(2^{x+2)}=186 ?

The answer to (4^{x-1})/(2^{x+2)}=186 is x=(ln(186))/(ln(2))+4

Solve for x: (4^{x-1})/(2^{x+2)}=186

The solution is x=(ln(186))/(ln(2))+4

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\frac{4 ^{x - 1}}{2 ^{x + 2}} = 186

x = \frac{ln ( 186 )}{ln ( 2 )} + 4

Decimal Notation

x = 11.53915 \dots

Solution steps

\frac{4 ^{x - 1}}{2 ^{x + 2}} = 186

Apply exponent rules

(2 (x - 1) - x - 2) ln (2) = ln (186)

Solve

(2 (x - 1) - x - 2) ln (2) = ln (186) : x = \frac{ln ( 186 )}{ln ( 2 )} + 4

x = \frac{ln ( 186 )}{ln ( 2 )} + 4

Verify Solutions:

x = \frac{ln ( 186 )}{ln ( 2 )} + 4

True

The solution is

x = \frac{ln ( 186 )}{ln ( 2 )} + 4

4 \cdot 7^{2 x} = 9

e^{x - 3} + e^{- x + 3} = 22

2^{9 x} = 5^{- x - 3}

e^{x + 1} = 9^{\frac{2 x}{3}}

e^{- x} - 2 x e^{x} = 0

What is the answer to (4^{x-1})/(2^{x+2)}=186 ?
The answer to (4^{x-1})/(2^{x+2)}=186 is x=(ln(186))/(ln(2))+4
Solve for x: (4^{x-1})/(2^{x+2)}=186
The solution is x=(ln(186))/(ln(2))+4