Question

if 2^x+1=3^1-x then find value of x​

Answer 1

Answer:

If 2^(x+1) = 3^(1-x) Then find the value of 'x'?

The given eqution is

2x+1=31−x

Taking log base 2 on both sides

(x+1)log2(2)=(1−x)log2(3)

x+1=log2(3)−x.log2(3)

x(1+log2(3))=log2(3)−1

x=log2(3)−11+log2(3)

What does x-1 equal?

What is x if 2x=3x−1 ?

What is the answer of this question: if 2^x=3^y=6^z,then what is the value of 1/x+1/y+1/z?

If 3^(x-1) + 3^(x+1) = 90 then what is the value of x?

If 2^x=3^y=6^-z, then what is (1/x+1/y+1/z) equal to?

Take log on both sides

(x+1)log2=(1-x)log3

Alternatively, (x+1)/(1-x)=log3/log2

Take componendo and dividendo on both sides:

2/2x=(log3+log2)/(log3-log2)

Take reciprocal,

X=(log3-log2)/(log3+log2)

Since the values for Log3=0.4771 and Log2=0.3010

x= 0.2263

Verification:

LHS=2^(1.2263)=2.3397

RHS=3^(0.7737)=2.3397

Answer 2

Answer:

$2 \times {2}^{x} = \frac{3}{ {3}^{x} }$

${6}^{x} = \frac{3}{2}$

$x = log_{6}( \frac{3}{2} )$