## mar1e0721 Group Title log 7 √ 49 2 years ago 2 years ago

1. satellite73

first off, $$\sqrt{49}=7$$ right?

2. mar1e0721

$\sqrt{7} 49$

3. satellite73

so you are being asked for $\log_7(7)$ which must be 1, because you are being asked "raise 7 to what power to get 7?" and the answer is 1

4. satellite73

now i am lost

5. satellite73

what is the base of your log? what is the input?

6. amorfide

if you have this as base 10 then you are multiplying 7 by 7=49 log49 but if it is base 7, follow what @satellite73 said

7. mar1e0721

log sqrt 7 bqase 49

8. mar1e0721

Base**

9. amorfide

lol what?

10. satellite73

$\log_{49}(\sqrt{7})$?

11. satellite73

base is 49, input is $$\sqrt{7}$$ right?

12. satellite73

trick is to try to write with exponents, because $\log_b(x)=y\iff b^y=x$ so you are trying to solve $49^y=\sqrt{7}$

13. satellite73

we see that $$49=7^2$$ and $$\sqrt{7}=7^{\frac{1}{2}}$$ so what you want is $7^{2y}=7^{\frac{1}{2}}$ or $2y=\frac{1}{2}$ or $y=\frac{1}{4}$

14. satellite73

meaning is simpler english that the number $$\sqrt{7}$$ is the fourth root of 49