Question

How to solve this maths equation with showing steps:​

Answer 1

Answer: x=1

Step-by-step explanation:

3^2x+9=10*3^x

3^2x/3^x= 10-9 (transferring like term to same sides)

3^x= 1

x=1

Answer 2

Given: An expression $3^{2x} + 9 = 10\times3^{x}$

To Find: The value of $x$

Solution:

$3^{2x} + 9 = 10\times3^{x}$

• Use $a^{mn} = (a^{n})^{m}$ to transform the expression.

$(3^{x})^{2}$$+ 9 = 10\times3^{x}$

• Solve the equation using substitution $t=3^{x}$.

$t^{2} + 9 = 10t$

• Rearrange the equation by taking $10t$ to the other side and hence, change its sign.

$t^{2} -10t+9 =0$

• Solve this by middle - term splitting method. Firstly, write $10t$ as a difference:

$t^{2} -t-9t+9 =0$

• Factor out $t$ from the expression:

$t\times(t-1)-9t+9=0$

• Factor out $-9$ from the expression.

$t\times(t-1) - 9(t-1) = 0$

• Factor out $(t-1)$ from the expression:

$(t-1)\times(t-9)=0$

• Separate into two cases:

$(t-1) = 0\\(t-9) = 0$

• Solve the equations by taking numbers to the other sides and thus, by changing their signs.

$t=0+1\\t=0+9$

• Add accordingly:

$t = 1\\t = 9$

• Now, substitute back $t = 3^{x}$.

$3^{x} = 1\\3^{x} = 9$

• Solve the equation for $x$.

$x = 0\\x = 2$

• Rewrite the above:

$x_1=0\\x_2=2$

Final Answer:

Hence, the two possible values of $x$ are $0$ and $2$.