What is the answer to solvefor x,t(x)=2.3^{x-1.5} ?

The answer to solvefor x,t(x)=2.3^{x-1.5} is x=-(\W(-\frac{ln(2.3))/(2.3^{1.5)t})}{ln(2.3)}

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solvefor x,t(x)=2.3^{x-1.5}

solve for

x, t (x) = 2. 3^{x - 1.5}

x = - \frac{W ( - \frac{l n ( 2.3 )}{2. 3 ^{1.5} t} )}{ln ( 2.3 )}

Solution steps

t (x) = 2. 3^{x - 1.5}

Prepare

t (x) = 2. 3^{x - 1.5}

for Lambert form:

t x e^{l n (2.3) (- x + 1.5)} = 1

Rewrite the equation with

- x ln (2.3) = u

and

x = - \frac{u}{ln ( 2.3 )}

t (- \frac{u}{ln ( 2.3 )}) e^{l n (2.3) (- (- \frac{u}{l n ( 2.3 )}) + 1.5)} = 1

Simplify

- \frac{e ^{u + 1.5 l n (2.3)} t u}{ln ( 2.3 )} = 1

Rewrite

- \frac{e ^{u + 1.5 l n (2.3)} t u}{ln ( 2.3 )} = 1

in Lambert form:

e^{u} u = - \frac{ln ( 2.3 )}{2. 3 ^{1.5} t}

Solve

e^{u} u = - \frac{ln ( 2.3 )}{2. 3 ^{1.5} t} : u = W (- \frac{ln ( 2.3 )}{2. 3 ^{1.5} t})

u = W (- \frac{ln ( 2.3 )}{2. 3 ^{1.5} t})

Substitute back

u = - x ln (2.3),

solve for

x

Solve

- x ln (2.3) = W (- \frac{ln ( 2.3 )}{2. 3 ^{1.5} t}) : x = - \frac{W ( - \frac{l n ( 2.3 )}{2. 3 ^{1.5} t} )}{ln ( 2.3 )}

x = - \frac{W ( - \frac{l n ( 2.3 )}{2. 3 ^{1.5} t} )}{ln ( 2.3 )}

4^{x - 2} = 3

1 8^{2 x - 3} = 2 0^{x + 1}

\frac{2 ^{x - 3}}{4 ^{1 - x}} = 1

625 (5^{x - 2}) - 5^{x} = 120

12 \cdot 1.1 7^{t} = 56

What is the answer to solvefor x,t(x)=2.3^{x-1.5} ?
The answer to solvefor x,t(x)=2.3^{x-1.5} is x=-(\W(-\frac{ln(2.3))/(2.3^{1.5)t})}{ln(2.3)}