3^x = 10 How do I solve this?

3^x=10
x ln(3) = ln(10)
x = 2.0959

...

x^3=10
x = 10^(1/3)
x = 2.1544

Take logs of both sides.

x log 3 = 1

x = 1/log 3

= 2.096

Remember the natural log identities:

a^x=xln(a)

Take the natural log of both sides and you should be able to figure out the rest for the first problem.

The second problem, x^3 = 10 is solved by taking the cube root of ten. It should turn out to be around 1.7 or 1.8 (don't have a calculator nearby).

Question 1
x log 3 = log 10
x log 3 = 1 (if base ten)
x = 1 / log 3
x = 2.096

Question 2
x³ = 10
3 log x = 1
log x = 1 /3
x = 10^(1/3)
x = 2.154

3^x = 10
x = log₃(10)
x = log(10)/log(3)
x ≈ 2.0959

Take the log. of both sides.
x^3 = 10
3* log(x) = log10

log(x) = 1/3
x = Anti.log(1/3) = 2.1544

ln is the natural log or log to the base e

There is a button on your calculator for it

3^x = 10
ln(3^x) = ln(10)
x ln3 = ln10
x = ln10 / ln 3

Although it is easier to solve this one using log to the base 10

Log to the base 10 of 10 = 1

3^x = 10
log(3^x) = log(10)
x log 3 = 1
x = 1 / log 3
put it into your calculator
x = 2.0959 (4dp)

x³ = 10

take the cube root of both sides
x = ³√10
x = 2.15443469 (8dp)

k wel since it is x to the 3 power you simple do the opposite which is the 3rd root of x. so you would also find the 3rd root of 10. you know the square root sign? it is the same thing but in front of the small line there is a 3 meaning the 3rd root so instead of finding a number times itself that equals 10 you would find a number to the 3rd power that = the number under the root sign in this case 10 since no exact number exists you would leave it as the 3rd root of 10 =x

it is the same thing as solving x^2=14(i just chose 14) you would find the square root of x^2 and 14. xtimesx=X^2 so x = the square root of 14. exept now it is x times x times x = 3rd root of 14


i hope that made sense.