Question

Please help me with logarithms!

Answer 1

x=2ln(2)/(2ln(2)-ln(3))

Explanation:

ln(4^x-1)=ln(3^x)

(x-1)ln(4)=ln(3^x)

(x-1)ln(4)=xln(3)

ln(4)x-ln(4)=xln(3)

ln(4)x=ln(3)x+2ln(2)

2ln(2)x-ln(3)x=2ln(2)

(2ln(2)-ln(3))x=2ln(2)

Therefore, x=2ln(2)/(2ln(2)-ln(3))

Answer 2

4.819 =x

Explanation:

4^(x-1) = 3^x

Take the log of each side

log (4^(x-1)) = log(3^x)

We know that log a^b = blog a

(x-1) log 4 = x log (3)

Distribute

x log 4 -log 4 = x log 3

Subtract x log 4 from each side

x log 4 - x log 4 -log 4 = x log 3 - x log 4

- log 4 = x log 3 - x log 4

Factor out -x

- log 4 =- x ( log 4- log 3)

Divide by -1

log 4 = x (log 4 - log 3)

Divide each side by (log 4 - log 3)

log 4 / (log 4 - log 3) = x

4.81884167930641800 =x

Round to the nearest thousandth

4.819 =x