Logarithms problems?

Question

1. log 3 (x^2y^3)
2. log 2 [(x^2+1)/(2^x)]
3. ln [(x^2 square root (x^2-1))/e^x]

Thx much

4. 2e^x+2=5

Answer 1

1. log 3 (x^2y^3)
Assuming you mean log 3 (x^2 * y^3)
log 3 (x^2y^3)
= log 3 (x^2) + log 3 (y^3)
= 2 log 3 x + 3 log 3 y

Otherwise log 3 (x^2y^3)
= 2y^3 log 3 x

2. log 2 [(x^2+1)/(2^x)]
= log 2 (x^2+1) - log 2 (2^x)
= log 2 (x^2+1) - x

3. ln [(x^2 square root (x^2 - 1))/e^x]
= ln (x^2) + ln (x^2 - 1)^½ - ln (e^x)
= 2ln x + ½ln(x^2 - 1) - x

4. 2e^x+2=5
So 2e^x = 3
ie e^x = 1.5
x = ln 1.5
≈ 0.4055

Answer 2

1. log3 x²y³
log3 x² + log3 y³
2 log3 x+ 3 log3 y

2. log2 x²+1/2^x
log2 (x² + 1) - log2 (2^x)
log2 (x² + 1) - x log2 (2)
log2 (x² + 1) - x

3. ln [(x^2 square root (x^2-1))/e^x]
ln x² (x² - 1)^½ / e^x
ln x² + ln (x² - 1)^½ - ln e^x
2 ln x + ½ ln (x² -1) - x ln e
2 ln x + ½ ln (x² - 1) - x

Answer 3

4. should be -1.084
3. cant understand it
2. cant undrstand
1. cant undrstand.

try being more specific. what is the base of the log? and stuff like that.