Question

Solve this equation 3^x= 3*2^x

Answer 1

Answer:

3^x = 3 × 2^x3^(x-1) = 2^x

Step-by-step explanation:

Answer 2

Step-by-step explanation:

3^x = 3 × 2^x

3^(x-1) = 2^x

now, let's apply the log of the base 2 to this.

log2(3^(x-1)) = x

logarithms of a specific base can be converted to logarithms of another base.

log b x = (log a x) / (log a b)

because I want to use log of the base 3 on the left hand side.

so,

log2(3^(x-1)) = log3(3^(x-1)) / log3(2) = (x-1)/log3(2)

(x-1)/log3(2) = x

x - 1 = x × log3(2)

x = x × log3(2) + 1

x(1 - log3(2)) = 1

x = 1/(1 - log3(2)) = 2.709511291...