Logarithmic Equations

Question

Solve for x. Please leave log in your answer.

1. 9^3x - 10 = 17
2. 11^-10x+ 7 = 54

Answer 1

9^3x - 10 = 17

Just like when you solve any equation, you always want to isolate the variable.

So, we start off by adding 10 to both sides.

9^3x = 27

Now, we want to "bring down" the 3x from the exponent.

Thus, we must take the logarithm base 9 to both sides of the equation.

3x = log₉ (27)

Finally, simply calculate.

3x = 3

x = 1

The second question is the same format, so I hope you can use these steps as a reference.

*Please feel free to ask me any question for clarification.

Answer 2

9^3x-10=17

9^3x=27

9=3^2 and 27=3^3

(3^2)^3x=3^3

3^6x=3^3

set the exponents equal to each other

6x=3

x=3/6=1/2

11^(-10x)+7=54

11^(-10x)=47

log(11^(-10x))=log47

-10xlog11=log47

-10x=log47/log11

-10x=1.672097858/1.041392685

-10x=1.605636262

x=1.605636262/(-10)

x=-0.1605636262 round as needed