Question
Solve the following equations:$3^{\text{x}+1}=27\times3^4$
✓
Answer
$3^{\text{x}+1}=27\times3^4$$\Rightarrow3^{\text{x}+1}=3^3\times3^4$
$\Rightarrow3^{\text{x}+1}+3^7$
$\Rightarrow\text{x}+1=7$
$\Rightarrow\text{x}=6$
$\Rightarrow3^{\text{x}+1}+3^7$
$\Rightarrow\text{x}+1=7$
$\Rightarrow\text{x}=6$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Simplify:$\Big(\frac{81}{49}\Big)^{-\frac{3}{2}}$
→Find the mode of the following data in each case:
7, 9, 12, 13, 7, 12, 15, 7, 12, 7, 25, 18, 7
7, 9, 12, 13, 7, 12, 15, 7, 12, 7, 25, 18, 7
Three persons can build a small house in 8 days. To build the same house in 6 days, how many persons are required?
In the following equations, find which variables x, y and z etc. represent rational or irrational numbers:
$x^2=5$
→$x^2=5$
Prove that, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also.
Given: line AB || line CD and line EF intersects them at P and Q respectively.
line EF ⊥ line AB
To prove: line EF ⊥ line CD
Examine whether the following numbers are rational or irrational.$3+\sqrt{3}$
→In a trapezium ABCD, AB || DC and M is the midpoint of BC. Through M, a line PQ || AD has been drawn which meets AB in P and DC produced in Q, as shown in the adjoining figure.
Prove that $\text{A}\text{(ABCD)}=\text{A}(\text{APQD}).$
→Prove that $\text{A}\text{(ABCD)}=\text{A}(\text{APQD}).$
Factorise:$\frac{3}{5}\text{x}^2-\frac{19}{5}\text{x}+4$
→Divide the first polynomial by the second polynomial and find the remainder using remainder theorem :
$\left(2 x^3-2 x^2+a x-a\right) ;(x-a)$
→$\left(2 x^3-2 x^2+a x-a\right) ;(x-a)$
Write the following in the expanded form:$\Big(\frac{\text{a}}{\text{bc}}+\frac{\text{b}}{\text{ca}}+\frac{\text{c}}{\text{ab}}\Big)^2$
→