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
Use the pythagorean theorem since it's a right triangle. 12 + r is the hypotenuse and r and 24 are the legs so r squared + 24 squared = (12 + r) squared. Simplify and get r squared plus 576 equals r squared + 24r +144. Subtract r squared from both sides and then subtract 144 from both sides. You're left with 432=24r. Divide both sides by 24. r=18
Answer: 9 ounces of granola and 6 ounces of raisins
Step-by-step explanation:
In this case you just divide the ounce that you been having previous in the ounces of 54 granolas then that gives you 9 because you divide 54/6 and that gives you 9 and the same as the other one you divide 36/6 and that give you 6