Question

Solve 3^(x+1)+3^(2x+1)=270

Answer 1

Answer:

3^(x+1)+3^(2x+1)=270

3^(x+1)+3^(2x+1)=3^3×10

X+1+2x+1=30

3x=28

x=28/3

Answer 2

The value of x is 2.

Explanation:

The given equation : $3^{x+1}+3^{2x+1}=270$

We can write 270 as $3\times3\times3\times2\times5=3^3\times10$

By using exponent property : $a^{m+n}=a^m\cdot a^n$

The equation becomes $3^{x+1}+3^{x+1+x}=3^3\times10$

$\Rightarrow\ 3^{x+1}+3^{x+1}3^x=3^3\times(1+9)$

Taking $3^{x+1}$ as common in LHS , we get

$3^{x+1}(1+3^x)=3^3(1+3^2)\ \ \ [\because\ 3^2=9]$

On Comparing both sides , we get

$x+1=3\text{ and } x=2$

That means x=2

Hence, the value of x is 2.

# Learn more :

If 3 power x= 270 then 3 power x-3=?

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