C2 Exponentials and Logarithms Help

1) Given that a = log(10)2 and b = log(10)3, find the expressions in terms of a and b for [(10) meaning a small 10]

a) log(10)1.5

OH yes I forgot bout that..I've just taught myself this topic as I was never taught this by a teacher so Im more likely to make mistakes with this topic...

Unfortunately for me, I've been set homework to do a whole sheet on Exponentials and Logarithms..

I think you should have been given log(10) 5

OK thanks guys..

But Im stuck on another question:
4log(3)x - 5 = 0
..

OK Thanks

Sorry to bother you guys again on this topic..
but i have another question:

log(3)x³ - 5log(3)x = 4

Is this right?
log(3)x³/5log(3)x = 4
1/5x² = 4
x² = 20
x = 4.472135955

I think you should have been given log(10) 5

log(10) 5 = 1 - log(10) 2

Oh ok thanks..man I'm going to really struggle with this worksheet and this whole topic in general ...

I don't even have an idea of how to work out this question:

An initial investment of £1000 is places into a savings account that offers 2.2% interest every 3 months. The amount of money in the account £P, at the end of t years is fiven by

P = 1000 X 1.022 ^(4t) ....( and that's a mutiply sign btw)

Find, to the nearest year, how long it will take for the investment to double in value. (4 marks)

.