Logarithms, solving for x?

Question

log3(x+9)=4 x= ?

note- 3 is down at the bottom

Studying for MPE for csu test. How do I solve this without caculator. I dont think I need law of logs but I understand the law of logs, so ya. Been sitting the whole summer doing no math. Forgot alot.

Answer 1

log is log to base 3:-
log (x + 9) = 4
x + 9 = 3^4
x + 9 = 81
x = 72

Answer 2

it is a property of logarithms that the base raised to the one beside the equal sign equals the antilogarithm. for example, log a b = c, where a is the base, then a^c = b.
for your case, it becomes 3^4 = x+9. since 3^4=81,
81=x+9 => x=72.

thus, x=72

Answer 3

You first would want to rewrite the equation:

log_3 (x+9) = 4 >>> 3^4 = x+9 (Definition of a logarithm)

Now you can solve it:

81 = x+9
72 = x

Answer 4

3^4 = x+ 9
x+9 = 81
x = 72

Answer 5

log_3 (x+9) = 4
<=> (x+9) = 3^4 = 81
so x = 81 - 9 = 72.

Answer 6

3^4=x+9
81=x+9
72=x

Answer 7

log(x+9)/log3 = 4
log(x+9) = 4log3
x+9 = 81
x = 72

Answer 8

log_3 (x + 9) = 4


change to exponent form. Remember this formula
log_b a = x <==> b^x = a

3^4 = x + 9

x = 3^4 - 9
x = 72

Answer 9

why base 10...it somewhat is stupid, i'm unlikely to try this: Take the organic log of the two components: ln(13^(3x)) = ln(sixteen^(-x - 2)) --> simplify utilising log(a^b) = b * log(a) 3x * ln(13) = (-x - 2) * ln(sixteen) --> distribute suitable section x * (3ln(13)) = -xln(sixteen) - 2ln(sixteen) --> upload xln(sixteen) to the two components x * (3ln(13) + ln(sixteen) = -2ln(sixteen) --> divide by utilising x's coefficient x = -2ln(sixteen) / (3ln(13) + ln(sixteen)) you will possibly desire to simplify that in case you like: 3ln(13) = ln(13³) = 2,197 --> ln(2197) + ln(sixteen) = ln(2,197 * sixteen) = ln(35,152) --> x = -2ln(sixteen) / ln(35,152) --> in case you elect for it in log??, then in basic terms positioned that throughout the time of for ln x = -2log??(sixteen) / log??(35,152) if certainty be told you will possibly desire to eliminate the log?? altogether when you consider that: x = -2 * log?????(sixteen)