Change Exponential Expression to Logs?

Question

Change each exponential expression to an equivalent expression involving a logarithm.

(1) 3^x = 4.6

(2) e^(2.2) = M

Answer 1

(1) 3^x = 4.6

x = log base 3 of 4.6

(2) e^(2.2) = M

2.2 = ln M

Remember that a logarithm is an exponent. This means that when you have an expression in exponential form, the exponent is going to be equal to something when you re-write the expression in logarithmic form.

Answer 2

To do this, the exponent becomes the coefficient of the log term. For example in the second problem, you can use Natural Logs and have
2.2 ln e = ln M
since ln e = 1, ln M =2.2

Answer 3

ok so 6 is the backside (abbreviated as 'b'), and six.5 is a extensive sort which I dont understand what to call, even though it is abbreviated as 'M'. it is a normal log expression: Log(base b)M = x. Now in simple terms plug the numbers in: Log(base 6)6.5 = x. And thats the respond =). substantial: once you write this on paper, the backside (b) is written as a subscript.

Answer 4

log(base 3) 4.6 = x
log(base e) M = 2.2

Answer 5

1) x = ln4.6 / ln3, since xln3 = ln4.6
2) 2.2 = lnM

Answer 6

x = ln(4.6) / ln(3)

2.2 = ln(M)