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The document is a worksheet for a mathematics course (Math 623) focused on logarithms and exponential functions. It includes various exercises where students are required to fill in blanks, rewrite expressions in exponential or logarithmic form, evaluate logarithmic functions, and solve equations involving logarithms. The worksheet aims to reinforce understanding of the properties and applications of logarithms.

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What is the logarithmic form of the exponential equation 4 3 5x 4?

The exponential equation 4^(3)=5x+4 can be written in logarithmic form as log4(5x+4) = 3. To convert the equation from exponential form to logarithmic form, we need to identify the base of the exponential expression (which is 4), the exponent (which is 3), and the result (which is 5x+4).

How to write exponential form to logarithmic form?

The exponential form ax=N a x = N is converted to logarithmic form logaN=x l o g a N = x . The exponent form of a to the exponent of x is equal to N, which on converting to logarithmic form we have log of N to the base of a is equal to x.

What is log n in exponential form?

The formula of log to exponential form is logaN=x l o g a N = x , is written in exponential form as ax=N a x = N . The logarithm of a number N to the base of a is equal to x, which if written in exponential form is equal to a to the exponent of x is equal to N.

What is log2 32 in exponential form?

What Is Log Base 2? Logarithmic FormExponential Form log216=4 24=16 log232=5 25=32 log264=6 l o g 2 64 = 6 26=64 2 6 = 64 log2128=7 l o g 2 128 = 7 27=128 2 7 = 1285 more rows

How do you write exponential form to logarithmic form?

The exponential form ax=N a x = N is transformed and written in logarithmic form as LogaN=x L o g a N = x . The exponential form of a to the exponent of x, which is equal to N is transformed to the logarithm of a number N to the base of a, and is equal to x.

How to write exponential and logarithmic functions?

We saw earlier that an exponential function is any function of the form f(x)=bx, where b0 and b1. A logarithmic function is any function of the form g(x)=logb(x), where b0 and b1. It is no coincidence that both forms have the same restrictions on b because they are inverses of each other.

What is solve 2x 32 and rewrite this equation in a logarithmic form?

A-Level Maths Tutor Summary: To solve 2^x = 32, we use logarithms to change the equation to x = log2(32). By applying the change of base formula with natural logarithms, we find x 4.9999. Since x represents an exponent and must be an integer, we round it to the nearest whole number, giving us x = 5.

How do you convert exponential forms?

An expression written in the exponential form can be easily converted to logarithmic form by using a simple formula: If ea = b, then logb l o g e b = a. Let us understand this conversion with the help of an example. Convert 5. By equating it with the formula given above, we can say that, here, b = 125, a = 3, and e = 5

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