What is 7^{log_{7}(4-2)log_{7}(2)}+3^{log_{3}(5)+log_{3}(2)}-2ln(e^3) ?

The solution to 7^{log_{7}(4-2)log_{7}(2)}+3^{log_{3}(5)+log_{3}(2)}-2ln(e^3) is 4+7^{log_{7}(2)^2}

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simplify 7^{log_{7}(4-2)log_{7}(2)}+3^{log_{3}(5)+log_{3}(2)}-2ln(e^3)

simplify

7^{l o g_{7} (4 - 2) l o g_{7} (2)} + 3^{l o g_{3} (5) + l o g_{3} (2)} - 2 ln (e^{3})

4 + 7^{l o g_{7} (2)^{2}}

Decimal Notation

5.28005 \dots

Solution steps

7^{l o g_{7} (4 - 2) l o g_{7} (2)} + 3^{l o g_{3} (5) + l o g_{3} (2)} - 2 ln (e^{3})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{3} (5) + lo g_{3} (2) = lo g_{3} (5 \cdot 2)

= 7^{l o g_{7} (2) l o g_{7} (4 - 2)} + 3^{l o g_{3} (5 \cdot 2)} - 2 ln (e^{3})

Multiply the numbers:

5 \cdot 2 = 10

= 7^{l o g_{7} (4 - 2) l o g_{7} (2)} + 3^{l o g_{3} (10)} - 2 ln (e^{3})

7^{l o g_{7} (4 - 2) l o g_{7} (2)} = 7^{l o g_{7} (2)^{2}}

3^{l o g_{3} (10)} = 10

2 ln (e^{3}) = 6

= 7^{l o g_{7} (2)^{2}} + 10 - 6

Add/Subtract the numbers:

10 - 6 = 4

= 4 + 7^{l o g_{7} (2)^{2}}

\frac{2}{3} lo g_{b} (x + 1) - \frac{1}{4} lo g_{b} (x + 2)

- lo g_{10} (4.6 \cdot 1 0^{7})

3 (ln (8) - ln (4))

2 ln (ln (x)) - ln (ln (x^{2}) + 1)

ln (\frac{e ^{\frac{0.8}{x}} - 1}{e ^{\frac{0.4}{x}} - 1})

What is 7^{log_{7}(4-2)log_{7}(2)}+3^{log_{3}(5)+log_{3}(2)}-2ln(e^3) ?
The solution to 7^{log_{7}(4-2)log_{7}(2)}+3^{log_{3}(5)+log_{3}(2)}-2ln(e^3) is 4+7^{log_{7}(2)^2}