How do l solve this one 2x=3(2 is raised to power x)?

2^x=3

log 2^x=log 3

by power rule
x log 2= log 3

so x=log 3/ log 2
x= 1.585

Use a graphing device to graph 2x - 3*2^x and find where it crosses the x intercept

http://www.coolmath.com/graphit/

NEVER!
No solution

Unless you wanted 2^x = 3??

take log of both sides

log(2^x) = log3
x log 2 = log 3
x = log 3 / log 2
x = 1.58 (2dp)

introducing log to both sides it gives
xlog2=log3

x=log3/log2.............dividing both sides by log2

2 raised to power x is written as 2^x

so we use the ln (or log decimals)

remember ln a^x = a * lnx

and x ln2 = ln 3

x= ln3/ln2=1.585

2^x = 3
x log 2 = log 3
x = log 3 / log 2
x = 1.585 (any log base may be used)

2^x = 3
x = log₂(3)
x = log(3)/log(2)
x ≈ 1.5849