exponential equation

So it seems that I've come to a standstill on a few problems I have for homework. This is my first time on this forum so I don't know how things work exactly. If you could tell me how to solve them or anything of that nature it would be greatly appreciated.

1.Solve the following exponential equation. Round your answer to 2 decimal places.

e^2x-e^x-2=0

2.Solve the logarithmic equation. Round to 2 decimal places

log base 2(x+1)-log base 2(x)=1

3.Solve the exponential equation. Round your answer to two decimal places if necessary.

6^(5-x)=15

Edit: I think I got this answer

5ln(6)-ln(15)/ln(6)

4. Write the expression as a sum and/or difference of logarithms. Express powers as factor.

ln(x^6/y^3z)

For this one I think I've got the answer but could you just double check it?

6lnx-3lny+lnz


Sorry if this is too much for my first post, but I'm not looking for answers, just some guidance on how to approach these problems.

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Originally Posted by Brokensound723

So it seems that I've come to a standstill on a few problems I have for homework. This is my first time on this forum so I don't know how things work exactly. If you could tell me how to solve them or anything of that nature it would be greatly appreciated.

1.Solve the following exponential equation. Round your answer to 2 decimal places.

e^2x-e^x-2=0

factor the left side ...

2.Solve the logarithmic equation. Round to 2 decimal places

log base 2(x+1)-log base 2(x)=1

put the logs together to form a single log expression, then change to an exponential equation

3.Solve the exponential equation. Round your answer to two decimal places if necessary.

6^(5-x)=15

Edit: I think I got this answer

[5ln(6)-ln(15)]/ln(6)

inserted the necessary grouping symbols


4. Write the expression as a sum and/or difference of logarithms. Express powers as factor.

ln(x^6/y^3z)

For this one I think I've got the answer but could you just double check it?

6lnx-3lny+lnz

should be -lnz

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Thanks got it (Happy)