Question

MHANIFA HELP ME 10 POINTS 3^x= 3*2^x solve this equation

Answer 1

Answer:

$\displaystyle x=\frac{\log 3}{\log(3)-\log 2}\approx 2.71$

Step-by-step explanation:

Logarithms

We need to recall these properties of logarithms:

$\log_ax^n=m\log_ax$

$\log_a(xy)=\log_a(y)+\log_a(y)$

The equation to solve is:

$3^x=3*2^x$

Applying logarithms:

$\log(3^x)=\log(3*2^x)$

Applying the exponent property on the left side and the product property on the right side:

$x\log(3)=\log 3+\log 2^x$

Applying the exponent property:

$x\log(3)=\log 3+x\log 2$

Rearranging:

$x\log(3)-x\log 2=\log 3$

Factoring:

$x(\log(3)-\log 2)=\log 3$

Solving:

$\boxed{\displaystyle x=\frac{\log 3}{\log(3)-\log 2}}$

Calculating:

$\mathbf{x\approx 2.71}$