Suppose that ln2=r. Use properties of logarithms to write the logarithm in terms of r.
ln32=__
To write ln 32 in terms of r, we can use the properties of logarithms.
First, let's express 32 as a power of 2.
32 = 2^5
Next, we can rewrite this expression using the property of logarithms that states that ln(a^b) = b * ln(a).
ln 32 = ln (2^5)
Using the property mentioned above, we can rewrite the expression as:
ln 32 = 5 * ln 2
Since we were given that ln 2 = r, we can substitute r for ln 2 in the equation:
ln 32 = 5r
Therefore, ln 32 in terms of r is 5r.
To write the logarithm in terms of r, we can use the properties of logarithms, specifically the power rule.
The power rule states that if we have a logarithm of a number raised to a power, we can rewrite it as the product of the power and the logarithm of the number. In other words:
log(a^b) = b * log(a)
Using this property, we can rewrite ln32 as follows:
ln32 = ln(2^5)
Since we already know that ln2 = r, we can substitute r into the equation:
ln32 = ln(2^5) = 5 * ln2 = 5 * r
Therefore, ln32 can be written in terms of r as 5r.
the expression is already written in terms of r
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