3^x=2
=> ln (3^x) = ln (2) [Taking Napierian Logarithm on both sides to make the equation linear]
=> x ln (3) = ln (2)
=> x = ln (2) / ln (3)
=> x = 0.631 [Approx. upto 3 decimal places]
Hi:
two way to do this
since 3 ^ 0 = 1 and 3^1 = 3
so your answer must be between 0 and 1
try 3^.5 which equal 1.732 050 807 569
3^.6 which 1.933 182 044 931763... closer
and through trail and error you get 0.630929753572... for a answer
another way is use logarithm
using the power rule of logarithm is
a^x = y so
log(y) / log(a) = x
so
y = 2 and a = 3 and we are finding x - using the rule like so
log(2) / log( 3) = x
0.301029995664/ .477121251966 = x
0.630929753572 = x
Proof or check :
3^x=2 - original equation
3^ 0.630929753572 = 2 - plugging x with 0.630929753572
2 = 2 - solving 3 ^ 0.630929753572
it checks and equals
I hope this helps
take the log of both sides. Log (3^x) = Log 2
= x(Log 3) = log 2
x=log2/log3
Take log of both side an get
log(3^x)=log2
or x log3=log2
and x= log2/log3
log(3^x) = log(2)
x log(3) = log(2)
x = log(2) / log(3)
x ≈ 0.6309
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Verified answer
3^x=2
=> ln (3^x) = ln (2) [Taking Napierian Logarithm on both sides to make the equation linear]
=> x ln (3) = ln (2)
=> x = ln (2) / ln (3)
=> x = 0.631 [Approx. upto 3 decimal places]
Hi:
two way to do this
since 3 ^ 0 = 1 and 3^1 = 3
so your answer must be between 0 and 1
try 3^.5 which equal 1.732 050 807 569
3^.6 which 1.933 182 044 931763... closer
and through trail and error you get 0.630929753572... for a answer
another way is use logarithm
using the power rule of logarithm is
a^x = y so
log(y) / log(a) = x
so
y = 2 and a = 3 and we are finding x - using the rule like so
log(2) / log( 3) = x
0.301029995664/ .477121251966 = x
0.630929753572 = x
Proof or check :
3^x=2 - original equation
3^ 0.630929753572 = 2 - plugging x with 0.630929753572
2 = 2 - solving 3 ^ 0.630929753572
it checks and equals
I hope this helps
take the log of both sides. Log (3^x) = Log 2
= x(Log 3) = log 2
x=log2/log3
3^x=2
Take log of both side an get
log(3^x)=log2
or x log3=log2
and x= log2/log3
log(3^x) = log(2)
x log(3) = log(2)
x = log(2) / log(3)
x ≈ 0.6309