1) 6^(3x)=104
loga =logarithm to the base a
loga n=z ⇔a^z=n
Therefore:
log6 104=3x
x=(log6 104) / 3
x=(ln 104) / 3ln 6=0.8640279....≈0.864 (loga z=ln a / ln z)
Answer: x≈0.864
2) log3 (x+2)+ log3 (4x-1)=5
log3 x=5 ⇔ 3⁵=x ⇒x=243
log3 [(x+2)(4x-1)]=log3 243
log3 (4x²+7x-2)=log3 243
Therefore:
4x²+7x-2=243
4x²+7x-245=0
we solve this square equation:
x=[-7⁺₋√(49+3920)] / 8 =(-7⁺₋63) / 8
we have two solutions:
x₁=(-7-63) / 8=-8.75 this solution is not valid.
x₂=(-7+63) /8=7
Answer: x=7
