write the equation in logarithm form
a) 343=7^3
b) 25-(1/5)-^2
c A=bc
Thank you for your help. I have no idea how to do this problem and I am getting stress.
a) just take logs of both sides. Since log(x^n) = n*logx, we have
log 343 = 3*log 7
Now, it would help to use base 7 for the logs, to make the nice and pretty equation
log7343 = 3
since 5^2 = 25, 5^-2 = 1/5^2 = 1/25
So, (1/5)^-2 = 1/(1/25) = 25
Using base 1/5 logs, that is
log1/525 = -2
A = bc
log A = log b + log c
Thank you very much Steve for explaining it like you did, that was a great help. It is greatly appreciated. Have a wonderful day.
Don't worry, I'll explain how to write each of these equations in logarithm form step by step. Remember that logarithms are the inverse operation of exponentiation, so they will help us rewrite the equations in a way that involves logarithms.
a) Starting with the equation 343 = 7^3, we want to rewrite it in logarithm form. In logarithm form, we have the base, the logarithm, and the value of the expression. The base is 7, the logarithm is what we're trying to find, and the value of the expression is 343.
To express the equation in logarithm form, we can write it as log(base 7) 343 = 3. So, the logarithm with base 7 of 343 is equal to 3.
b) Considering the equation 25 - (1/5)^2, we can simplify it by performing the exponentiation first. Remember that squaring a fraction means squaring both the numerator and the denominator. So, (1/5)^2 = 1^2 / 5^2 = 1/25.
Now we can rewrite the equation as 25 - 1/25. To express this equation in logarithm form, we need to find the base, the logarithm, and the value of the expression. Since there is no clear logarithmic relationship here, logarithms might not be applicable in this case. It seems that the equation is already in its simplified form.
c) Lastly, we have the equation A = bc. To convert it into logarithm form, we need to identify the base, the logarithm, and the value of the expression. However, in this case, logarithms are not necessary as the equation is already in a standard algebraic form.
In summary:
a) log(base 7) 343 = 3
b) No logarithmic form applicable
c) Already in standard algebraic form